Presentation Transcript

1. Triangles in GeometryClick anywhere to start!

   By: Samantha Alberts
2. Audience 9th-10th graders Middle class suburban community Students who are studying for a test over triangles in geometry. Visual and kinesthetic learners Students who can regulate their own learning by adjusting their pace and amount of time on the lesson. Students who understand how to use a computer.
3. Learning Environment Individually At a computer, during class In a computer lab calculator, pencil, and paper. In a place where learning and talking to oneself is allowed. Teacher walking around to aide when aide is needed.
4. Objective (1) After reviewing the different types of triangles, students will be able to identify them with 100% accuracy.
5. Objective (2) After reviewing the trigonometric functions students will be able to recognize how to use them with 95% accuracy.
6. Objective (3) After reviewing the Pythagorean Theorem, the law of sines, and the law of cosines students will be able to demonstrate how to use each one with 85% accuracy.
7. Objective (4) After going over special triangles students will be able to recognize them with 90% accuracy.
8. Objective (5) Upon completion of this lesson students will be able to identify key types of triangles, special triangles, Pythagorean theorem, law of sines, and law of cosines with 80% accuracy.
9. Objective (6) Upon completion of this lesson students will be prepared for their test on triangles by answering 80% of the quiz questions correctly.
10. Motivation activity Do you think geometry is hard? Or that triangles are difficult? I have a solution. This lesson will allow all your questions to be answered. If not then you will receive a piece of candy for every question related to the material that will be on your test next week.
11. Orientation activity In geometry triangles are very important. You will use them in almost all your math classes from here on. Make sure you pay attention to all the information. There will be a quiz at the end. Also, half the questions in the quiz will be on your test next week.
12. Directions(please read all) Read through all the different information about each different section we covered in this part of the semester. Make sure you understand the material before going on to the next part, if that means you need to use your calculator, pencil, and paper then do so. You will later on in the lesson. Answer all the questions to the best of your ability. If you do well you are ready for the test. If not then go back over what you did not understand. Ask any questions when you have them.
13. Help! This is the help page. Each button you see here will show up on other pages at the bottom. = back button Forward button= = Home button Home
14. Home Page Pythagorean Theorem/ Non-right Triangles Interior & Exterior Angles Different Types of Triangles Special Triangles Right Triangles Quiz
15. Interior & Exterior Angles An interior angle is inside the triangle. An exterior angle is created by extending any side of the triangle to the outside. Home
16. Interior & Exterior Angles Home
17. Interior & Exterior Angles The sum of all three interior angles in any triangle will always add up to 180˚. Home
18. Interior & Exterior Angles ∠A=60˚ ∠D=120˚ Also, the sum of the interior angle and its exterior angle will always add up to be 180˚. 120˚ ∠A+∠D= 180˚ 60˚+120˚= 180˚ D A 60˚ Home
19. Interior & Exterior Angles Question(Click on the answer you think it is) Is the interior angle the outside or inside angle of a triangle? A) Outside B) Inside
20. Interior & Exterior Angles Question: Answer A) Outside INCORRECT. The interior angle is actually the inside angle of a triangle.
21. Interior & Exterior Angles Question: Answer B) Inside CORRECT! The interior angle is the inside angle of a triangle.
22. Interior & Exterior Angles Question(Click on the answer you think it is) Are the interior angle and exterior angle of a triangle equal to 180˚? A) Yes B) No
23. Interior & Exterior Angles Question: Answer A) Yes CORRECT! The interior angle and the exterior angle added together equal 180˚
24. Interior & Exterior Angles Question: Answer B) No INCORRECT! The interior angle and the exterior angle added together do equal 180˚
25. Different Types of Triangles Equilateral Triangle: - Will always have 3 equal sides. Those sides will have equal angles. Those angles will always be 60˚. Home
26. Different Types of Triangles Isosceles Triangle: - This triangle will always have 2 equal sides. Those 2 sides will always have the same angle. Home
27. Different Types of Triangles Scalene Triangle: -Will never have any sides or angles the same. Home
28. Different Types of Triangles Acute Triangle: -Will have every interior angle be less than 90˚ <90˚ Home
29. Different Types of Triangles Obtuse Triangle: -Has one angle that is more than 90˚ Home
30. Different Types of Triangles Question(Click on the answer you think it is) Is this an equilateral triangle? A) Yes B) No
31. Different Types of Triangles Question: Answer A) Yes You are incorrect. Since the angles are different it is not an equilateral triangle. The triangle is actually an acute triangle.
32. Different Types of Triangles Question: Answer B) No You are correct. An equilateral triangle has all the same angles. This triangle did not have all the same angles. It is actually an acute triangle.
33. Different Types of Triangles Question(Click on the answer you think it is) Is this an acute triangle? A) yes B) No
34. Different Types of Triangles Question: Answer A) Yes Oops! This triangle is actually an obtuse triangle. An acute triangle is actually less than 90˚
35. Different Types of Triangles Question: Answer B) No Great job! You knew this was an obtuse triangle and not an acute triangle.
36. Right Triangles Right Triangle: - Has one angle that is exactly 90˚ 90˚ Home
37. Right Triangles Right Isosceles Triangle: - Has a right angle, as well as 2 equal angles that are 45˚ each. 45˚ 90˚ Home
38. Right Triangles In right triangles, the trigonometric rations of sine, cosine, and tangent can be used to find unknown angles and the lengths of unknown sides. Home
39. Right Triangles Home
40. Right Triangles SinA= Opposite/ Hypotenuse Which equals =a/c Home
41. Right Triangles CosA= Adjacent/ Hypotenuse Which equals =b/c Home
42. Right Triangles TanA= Opposite/Adjacent Which equals =a/b Home
43. Right Triangles “SOH-CAH-TOA” is easier to remember for sine, cosine, and tangent. SOH=> sin=opposite/hypotenuse CAH=> cos=adjacent/hypotenuse TOA => tan=opposite/adjacent Home
44. Right Triangles CscA is the complete opposite of SinA so CscA=Hypotenuse/Opposite Which equals =c/a Home
45. Right Triangles SecA is the complete opposite of CosA so SecA= Hypotenuse/adjacent Which equals =c/b Home
46. Right Triangles CotA is the complete opposite of TanA so CotA=Adjacent/Opposite Which equals =b/a Home
47. Right Triangles Question(Click on the answer you think it is) Is the SinH=A/C A) Yes B) No
48. Right Triangles Question: Answer A) Yes CORRECT! The SinH is opposite/hypotenuse= A/C
49. Right Triangles Question: Answer B) No INCORRECT. The SinH is equal to A/C, which is opposite/hypotenuse.
50. Right Triangles Question(Click on the answer you think it is) Is the CotH=B/A A) Yes B) No
51. Right Triangles Question: Answer A) Yes That’s Correct! The CotH is equal to B/A or Adjacent/Opposite
52. Right Triangles Question: Answer B) No That’s Incorrect! The CotH is equal to B/A or Adjacent/Opposite
53. Right Triangles Question(Click on the answer you think it is) Is this triangle a right or right isosceles triangle? A) Right Isosceles B) Right
54. Right Triangles Question: Answer A) Right Isosceles Oops! It might look like a right isosceles triangle but the sides are not the equal and neither are the angles so it is actually a right triangle.
55. Right Triangles Question: Answer B) Right Great job! You know that it was a right triangle because none of the sides or angles are the same.
56. Pythagorean Theorem/ Non-right Triangles The Pythagorean Theorem is an equation that is used for right triangles only. It is used to find either a side or the hypotenuse. a and b are the sides or “legs” of the triangle and c is the hypotenuse. Home
57. Pythagorean Theorem/ Non-right Triangles To use the Pythagorean Theorem you must identify the missing information. For example: You have the triangle with the information of b=4, a=3, and c=? What is c? ? 3 4 Home
58. Pythagorean Theorem/ Non-right Triangles So you know that the Pythagorean Theorem is: c²=a²+b² You now plug in what you know from the given information. c²=3²+4² Home
59. Pythagorean Theorem/ Non-right Triangles You then find the squares of 3 and 4 to get: c²=9+16 Then you add 9 and 16 together c²=25 Square root both sides √(c²)= √25 Your answer is: C=5 This is how you use the Pythagorean Theorem. Home
60. Pythagorean Theorem/ Non-right Triangles Along with an equation for right triangles there are other equations for non-right triangles. These equations are called the law of sines and the law of cosines. The law of sines is useful for computing the lengths of the unknown sides in a triangle if two angles and one side are known. Home
61. Pythagorean Theorem/ Non-right Triangles The equation for the law of sines is: sin A= sin B= sin C abc Home
62. Pythagorean Theorem/ Non-right Triangles How to use the law of sines. If you have a non-right triangle with the known information of: A=60˚, B=80˚, C=40˚, a=6, b=?, c=? What do you do first? Let’s look and see. Home
63. Pythagorean Theorem/ Non-right Triangles We are first going to find b then later we will find c. So we have the equation for law of sines. (You do not have to use the sin A = sin B whole equation) ab Then plug in what you know. sin 60 = sin 80 6 b Home
64. Pythagorean Theorem/ Non-right Triangles You’re going to cross multiply to get: sin 60 = sin 80 Sin60b=Sin80(6) 6 b Which equals: Sin60b=5.9 Going to divide by Sin60 b=5.9/Sin 60 so the answer is: b=6.8 Home
65. Pythagorean Theorem/ Non-right Triangles Then you need to solve for c by using either a or b to complete the triangle. Let’s use a because it was used in the problem to begin with and we know that it is correct. So you have: sin A= sin CSin60 =Sin40 ac 6 c Home
66. Pythagorean Theorem/ Non-right Triangles You’re going to cross multiply to get: sin 60 = sin 40 Sin60c=Sin40(6) 6 c Which equals: Sin60c=3.9 Going to divide by Sin60 c=3.9/Sin 60 so the answer is: c=4.5 Home
67. Pythagorean Theorem/ Non-right Triangles Along with the law of sines there is another equation known as the law of cosines, which can only be used for non-right triangles. The law of cosines can be used to determine a side of a triangle if two sides and the angle between them are known. It can also be used to find the cosine of an angle if the lengths of all the sides are known. There are three equations for the law of cosines. Home
68. Pythagorean Theorem/ Non-right Triangles The law of cosines. c²=a²+b²-2abCosC This equation would be used to find the missing side c. Home
69. Pythagorean Theorem/ Non-right Triangles How to use the law of cosines. For example you are given the following information. a=6, b= 2, CosC=56˚ You would use this equation to find c. Home
70. Pythagorean Theorem/ Non-right Triangles You first plug in what you know from the information. c²=6²+2²-2(6)(2)Cos56 You simplify the equation c²=36+4-24Coc56 You simplify even more to get c²=40-14.11 Simplify one more time c²= 25.89 so the answer is C=5.09 Square root both sides √(c²)= √(25.89) Home
71. Pythagorean Theorem/ Non-right Triangles There are two other equations for the law of cosines. Depending on what you are missing. If you are missing side a in the triangle the equation is a²= b²+c²-2bcCosA If you are missing side b in the triangle the equation is b²= a²+c²-2acCosB Home
72. Pythagorean Theorem/ Non-right Triangles Question(Click on the answer you think it is) Do you use the Pythagorean Theorem for right triangles or non-right triangles? A) Right B) Non-right
73. Pythagorean Theorem/ Non-right Triangles Question: Answer A) Right CORRECT! You do use the Pythagorean Theorem for right triangles.
74. Pythagorean Theorem/ Non-right Triangles Question: Answer B) Non-right INCORRECT. The only time you do not use the Pythagorean Theorem is with non-right triangles.
75. Pythagorean Theorem/ Non-right Triangles Question(Click on the answer you think it is) Is this the equation for law of sines? sin A= sin B= sin C bca A) Yes B) No
76. Pythagorean Theorem/ Non-right Triangles Question: Answer A) Yes Oops! The law of sines equation is actually: sin A= sin B= sin C abc
77. Pythagorean Theorem/ Non-right Triangles Question: Answer B) No Great job! You know that this is not the correct equation. The correct equation is: sin A= sin B= sin C abc
78. Pythagorean Theorem/ Non-right Triangles Question(Click on the answer you think it is) If you were suppose to use the law of cosines to find b, would you use this equation? b²=a²-c²+acCosB A) Yes B) No
79. Pythagorean Theorem/ Non-right Triangles Question: Answer A) Yes That’s incorrect. The real equation is b²=a²+c²-acCosB
80. Pythagorean Theorem/ Non-right Triangles Question: Answer B) No That’s correct. The real equation is b²=a²+c²-acCosB
81. Special Triangles There are a couple of special triangles that you will need to be aware of for your test next week. Home
82. Special Triangles There is a special triangle with angles of 45-45-90. Which is called a 45-45-90 triangle. Which will always have a side ratio of 1:1:√2 Home
83. Special Triangles Another special triangle that you need to know of is a 30-60-90 triangle. Which will always havea side ratio of 1:√3:2 Home
84. Special Triangles There are also what we call “Pythagorean Triples” which are special triangles that will always be the same. Even their multiples are special triangles. Home
85. Special Triangles Here are the three main Pythagorean Triples 3:4:5 5:12:13 8:15:17 But don’t forget that their multiples work too! 6:8:10 10:24:26 16:30:34 Home
86. Special Triangles Question(Click on the answer you think it is) Does one of the special triangles have a side ratio of 1:1:√2? A) Yes B) No
87. Special Triangles Question: Answer A) Yes CORRECT! The side ratio 1:1: √2 is that of a 45-45-90 triangle.
88. Special Triangles Question: Answer B) No INCORRECT! The side ratio 1:1: √2 is that of a 45-45-90 triangle, which is a special triangle.
89. Special Triangles Question(Click on the answer you think it is) Which one of these ratios is a Pythagorean Triple? A) 5:3:5.8 B) 3:4:5
90. Special Triangles Question: Answer A) 5:3:5.8 Oops! The side ratio 5:3:5.8 is not a Pythagorean Triple.
91. Special Triangles Question: Answer B) 3:4:5 Great job! The side ratio 3:4:5 is a Pythagorean Triple.
92. Quiz Directions (Please read all) Before taking the quiz make sure you have a calculator, pencil, and paper. Once you start the quiz you can not go back till after the quiz is over. Also, keep track of which ones you get right and which ones you get wrong. You might see some of these questions on your test. Click here to being the quiz
93. Question 1(click on your answer) What type of triangles are these? A) Equilateral B) Isosceles C) Scalene D) Right
94. Question 1 Answer Oops! You chose A) Equilateral But an equilateral triangle has all the sides and angles equal to one another. These triangles has no equal sides or angles. Try again
95. Question 1 Answer Oops! You chose B) Isosceles If you remember from the lesson an isosceles triangle has two equal sides and angles. These triangles have no equal sides or angles. Try again
96. Question 1 Answer You’re Right! You chose C) Scalene A scalene triangle does not have any equal sides or angles! Question 2
97. Question 1 Answer Oops! You chose D) Right Remember that a right triangle has one angle that is 90˚ like this. These triangles in the question have no sides or angles that are the same or an angle that is 90˚ Try again
98. Question 2(click on your answer) What type of triangle is this? A) Acute B) Right C) Obtuse
99. Question 2 Answer Great job! You chose A) Acute You know that an acute triangle had all its interior angles less than 90˚ Question 3
100. Question 2 Answer Uh oh! You chose B) Right A right triangle has one angle that is 90˚. This triangle has all angles less than 90˚ Try Again
101. Question 2 Answer Uh oh! You chose C) Obtuse An obtuse triangle has one angle that is more than 90˚. This triangle is less than 90˚. Try Again
102. Question 3(Click on your answer) What type of triangles are these? A) Obtuse B) Acute C) Right
103. Question 3 Answer You are incorrect. You chose A) Obtuse An obtuse triangle has one angle that is more than 90˚. These triangles have one angle that is exactly 90˚ each. Try Again
104. Question 3 Answer You are incorrect. You chose B) Acute An acute triangle is less than 90˚. These triangles are exactly 90˚. Try Again
105. Question 3 Answer You are correct. You chose C) Right A right triangle has one angle that is exactly 90˚. Question 4
106. Question 4(click on your answer) What type of triangle is this? A) Isosceles B) Right C) Scalene D) Equilateral
107. Question 4 Answer That’s not right. You chose A) Isosceles An isosceles triangle has only two sides and two angles that are the same. This triangle has all three sides and all three angles the same. Try Again
108. Question 4 Answer That’s not right. You chose B) Right A right triangle has a 90˚angle. This triangle has no 90˚angle. In fact every side and angle are equal to one another. Try Again
109. Question 4 Answer That’s not right. You chose C) Scalene A scalene triangle has no sides or angles that are the same. This triangle has all congruent sides and angles, means they are all the same. Try Again
110. Question 4 Answer That’s right. You chose D) Equilateral An equilateral triangle has all congruent sides and angles, meaning they are all equal to each other. Question 5
111. Question 5(click on your answer) What type of triangle is this? A) Obtuse B) Acute C) Right
112. Question 5 Answer That’s Right! You chose A) Obtuse An obtuse triangle has an angle that is more than 90˚. Question 6
113. Question 5 Answer That’s incorrect. You chose B) Acute An acute triangle has all its angles less than 90˚. This triangle has one angle that is more than 90˚. Try Again
114. Question 5 Answer That’s incorrect. You chose C) Right A right triangle has an angle that is exactly 90˚. This triangle has an angle that is more than 90˚. Try Again
115. Question 6(click on your answer) What type of triangle is this? A) Scalene B) Isosceles C) Right D) Equilateral
116. Question 6 Answer That is incorrect. You chose A) Scalene A scalene triangle has no sides or angles that are the same. This triangle has two sides and two angles that are the same. Try Again
117. Question 6 Answer That is Correct. You chose B) Isosceles An isosceles triangle has two sides and two angles that are the same. Question 7
118. Question 6 Answer That is incorrect. You chose C) Right A right triangle has one angle that is exactly 90˚. This triangle has no angle that is 90˚. Try Again
119. Question 6 Answer That is incorrect. You chose D) Equilateral An equilateral triangle has all three sides and all three angles the same. This triangle has only two sides and two angles that are the same. Try Again
120. Question 7(click on your answer) What does SOH-CAH-TOA stand for? A) Some - Canned - Tofu B) Sin= opp/hyp - Cos=adj/hyp - Tan=opp/adj C) Symmetric - Congruent - Tangent
121. Question 7 Answer That’s not right. You chose A) Some-Canned-Tofu Someone’s not been paying attention. I think you are thinking about lunch. Try Again
122. Question 7 Answer That’s right. You chose B) Sin= opp/hyp-Cos=adj/hyp-Tan=opp/adj SOH-CAH-TOA stands for how to find the different sides of a right triangle. Question 8
123. Question 7 Answer That’s not right. You chose C) Symmetric-Congruent-Tangent I can see where it might mean this. However, that isn’t what SOH-CAH-TOA stands for. Try Again
124. Question 8(click on your answer) What is the sinA? B A) 4/5 5 B) 3/5 4 C) 3/4 D) 5/4 C A 3
125. Question 8 Answer You’re correct! You chose A) 4/5 4/5 is the sinA Question 9
126. Question 8 Answer You’re incorrect You chose B) 3/5 3/5 is actually the CosA not the SinA Try Again
127. Question 8 Answer You’re incorrect You chose C) 3/4 3/4 is the TanA not the SinA Try Again
128. Question 8 Answer You’re incorrect You chose D) 5/4 5/4 is the CscA not the SinA Try Again
129. Question 9(click on your answer) What is the TanC? C 1 B A) 1/√3 B) 2/√3 √3 2 C) √3/1 D) √3/2 A
130. Question 9 Answer That’s not quite right You chose A) 1/√3 1/√3 is the CotC not the TanC Try Again
131. Question 9 Answer That’s not quite right You chose B) 2/√3 2/√3 is the CscC not the TanC Try Again
132. Question 9 Answer That’s right You chose C) √3/1 √3/1 is the TanC Question 10
133. Question 9 Answer That’s not quite right You chose D) √3/2 √3/2 is the SinC not the TanC Try Again
134. Question 10(click on your answer) What is the SecB? C 6 A A) 6/10.8 B) 10.8/6 10.8 9 C) 9/10.8 B D) 10.8/9
135. Question 10 Answer Oops! You chose A) 6/10.8 6/10.8 is the SinB not the SecB Try Again
136. Question 10 Answer Oops! You chose B) 10.8/6 10.8/6 is the CscB not the SecB Try Again
137. Question 10 Answer Oops! You chose C) 9/10.8 9/10.8 is the CosB not the SecB Try Again
138. Question 10 Answer Yay! You chose D) 10.8/9 10.8/9 is the SecB Question 11
139. Question 11(click on your answer) What is the CscA? A) 5/4 B B)5/3 5 4 C) 4/5 A 3 C D) 4/3
140. Question 11 Answer Correct! You chose A) 5/4 5/4 is the CscA Question 12
141. Question 11 Answer That is incorrect. You chose B) 5/3 5/3 is the SecA not the CscA. Try Again
142. Question 11 Answer That is incorrect. You chose C) 4/5 4/5 is the SinA not the CscA. Try Again
143. Question 11 Answer That is incorrect. You chose D) 4/3 4/3 is the TanA not the CscA. Try Again
144. Question 12(click on your answer) Use the Pythagorean Theorem to find the missing side. B A) 16 17 B) 8 15 C) 9 C A ?
145. Question 12 Answer That’s not quite right You chose A) 16 16 is not the missing side. Try to use the Pythagorean Theorem again. Try Again
146. Question 12 Answer That’s right You chose B) 8 8 is the missing side of this triangle. This triangle is also a Pythagorean Triple if you remember. Question 13
147. Question 12 Answer That’s not quite right You chose C) 9 9 is not the missing side. Try to use the Pythagorean Theorem again. Try Again
148. Question 13(click on your answer) Find the missing information using the Law of Sines. A=60˚ a=6 B=80˚ b=6.8 C= 40˚ c=? A) 4.5 B) 5 A b c C) 4.7 B C a
149. Question 13 Answer Great job! You chose A) 4.5 4.5 is the missing side. Question 14
150. Question 13 Answer Uh oh! You chose B) 5 5 is not the missing side. Try to use the law of sines again start with; Sin60 = Sin40 6 c Try Again
151. Question 13 Answer Uh oh! You chose C) 4.7 4.7 is not the missing side. Try to use the law of sines again start with; Sin60 = Sin40 6 c Try Again
152. Question 14(click on your answer) Use the law of cosines to find the missing information. What is a equal to? A) 255.6 6 55˚ B) 257 15 a C) 259.7
153. Question 14 Answer Oops! You chose A) 255.6 255.6 is not the missing side. Try to use the law of cosines again start with; a²=6²+15²-2(6)(15)Cos55 Try Again
154. Question 14 Answer Great job! You chose B) 257 257 is the missing side. Question 15
155. Question 14 Answer Oops! You chose C) 259.7 259.7 is not the missing side. Try to use the law of cosines again start with; a²=6²+15²-2(6)(15)Cos55 Try Again
156. Question 15(click on your answer) Which angle is the exterior angle? A) ∠A B B) ∠B C) ∠C D A C D) ∠D
157. Question 15 Answer Uh Oh! You chose A) ∠A ∠A is an interior angle not an exterior angle. Try Again
158. Question 15 Answer Uh Oh! You chose B) ∠B ∠B is an interior angle not an exterior angle. Try Again
159. Question 15 Answer Uh Oh! You chose C) ∠C ∠C is an interior angle not an exterior angle. Try Again
160. Question 15 Answer Awesome job! You chose D) ∠D ∠D is an exterior angle. Question 16
161. Question 16(click on your answer) What do all the interior angles add up to? A) 90 B) 180 C) 270 D) 360
162. Question 16 Answer That’s not quite right. You chose A) 90 90 is to small for all the interior angles to add up to because you can have one interior angle that is 90 or larger. Try Again
163. Question 16 Answer That’s right. You chose B) 180 180 is what all the interior angles add up to be. Question 17
164. Question 16 Answer That’s not quite right. You chose C) 270 270 is to large for all the interior angles to add up to. Try Again
165. Question 16 Answer That’s not quite right. You chose D) 360 360 is to big for all the interior angles to add up to. Try Again
166. Question 17(click on your answer) If you have an interior angle of 39˚ what is your exterior angle? A) 51˚ B) 141˚ C) 231˚ D) 321˚
167. Question 17 Answer You‘re incorrect You chose A) 51˚ 51˚ only makes 90˚ which is to small. Try Again
168. Question 17 Answer You‘re correct You chose B) 141˚ 141˚ is what the exterior angle is. Question 18
169. Question 17 Answer You‘re incorrect You chose C) 231˚ 231˚ is to much for the exterior angle to be. Try Again
170. Question 17 Answer You‘re incorrect You chose D) 321˚ 321˚ is to much for the exterior angle to be. Try Again
171. Question 18(click on your answer) What is the ratio for a 45-45-90 triangle? A) 1:√3:2 B) 7:15:18 C) 1:1:√2 D) 3:4:5
172. Question 18 Answer Oops! You chose A) 1:√3:2 1:√3:2 is a special triangle ratio, but not for a 45-45-90 triangle. Try Again
173. Question 18 Answer Oops! You chose B) 7:15:18 7:15:18 is not a possible triangle. Try Again
174. Question 18 Answer Great job! You chose C) 1:1:√2 1:1:√2 is the ratio for a 45-45-90 triangle. Question 19
175. Question 18 Answer Oops! You chose D) 3:4:5 3:4:5 triangle is a special triangle but its angles are not 45-45-90 Try Again
176. Question 19(click on your answer) What is the ratio of a 30-60-90 triangle? A) 1:√3:2 B) 1:1:√2 C) 8:15:17 D) 3:4:5
177. Question 19 Answer You‘re right. You chose A) 1:√3:2 1:√3:2 is the ratio of a 30-60-90 triangle. Question 20
178. Question 19 Answer You‘re not right. You chose B) 1:1:√2 1:1:√2 is the ratio of a 45-45-90 triangle. Try Again
179. Question 19 Answer You‘re not right. You chose C) 8:15:17 8:15:17 is a special triangle but its not the ratio of a 30-60-90 triangle. Try Again
180. Question 19 Answer You‘re not right. You chose D) 3:4:5 3:4:5 is a special triangle but its not the ratio of a 30-60-90 triangle. Try Again
181. Question 20(click on your answer) Is a 32:60:68 triangle a Pythagorean Triple? A) Yes B) No
182. Question 20 Answer Yay! You chose A) Yes 32:60:68 is the same triangle as 8:15:17 just multiplied by 4
183. Question 20 Answer Uh oh! You chose B) No 32:60:68 is the same triangle as 8:15:17, which is a Pythagorean Triple, it’s just multiplied by 4
184. Since You finished! Here is a video to show another way to remember the Pythagorean Theorem.
185. Congrats You’ve Finished the Quiz!Let’s see how you did! If you got 20 right you’re amazing! If you got 17-19 right you’re very smart! If you got 14-16 right you did a good job. If you got 10-13 right you need to go over something in the lesson again. If you got 0-9 right go back through the information and try again.
186. You got 14-20 Questions Right! You know your triangles! Please come see me to find out what you need to do next. Home
187. You got 0-13 Questions Right Need to go back over something you didn’t know or understand? Click the home button to go back to the home page. Also, ask questions if you don’t understand where you went wrong. Home