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Quarterly Assessment # 2

Quarterly Assessment # 2. Assessment 2 Geometry Answers. Review QA # 1. “If a quadrilateral has four equal sides, then that quadrilateral is a square.” Draw me a counterexample to the statement above. Which of the following best describes the triangle below? Are they congruent? Similar?.

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Quarterly Assessment # 2

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  1. Quarterly Assessment # 2 Assessment 2 Geometry Answers

  2. Review QA # 1 • “If a quadrilateral has four equal sides, then that quadrilateral is a square.” Draw me a counterexample to the statement above. • Which of the following best describes the triangle below? Are they congruent? Similar? They are similar Not Congruent 35° 6 6 35° 3 3

  3. Review QA # 2 • Draw me 2 shapes that are similar but NOT congruent? • Are these shape Similar? Congruent? a. b. c. d. a. Congruent b. Neither c. Congruent d. Similar

  4. 4 7 ? Review QA # 3 3<X<11, Perimeter : 14<y<22 • A triangle has sides with lengths of 4 and 7 inches. Which of the following could be the perimeter of the triangle? • A triangle has sides with lengths of 7 and 10 inches. Which of the following could be the perimeter of the triangle? 3. A triangle has sides with lengths of 11 and 17 inches. Which of the following could be the perimeter of the triangle? 3<X<17, Perimeter: 20<y<34 6<X<28, Perimeter: 34<y<56

  5. 3 12 ? Bell Work • A triangle has sides with lengths of 3 and 12 inches. Which of the following could be the perimeter of the triangle? • A triangle has sides with lengths of 6 and 10 inches. Which of the following could be the perimeter of the triangle? 3. A triangle has sides with lengths of 10 and 17 inches. Which of the following could be the perimeter of the triangle? 9<X<15, Perimeter: 24<y<30 4<X<16, Perimeter: 20<y<32 7<X<27, Perimeter: 34<y<54

  6. 3x + 43 x + 55 6x + 43 4x + 43 5x + 15 5x + 60 5x + 13 8x + 13 Review QA # 4 X= 17, 1-side = 145 • What is the length of a side of the square below? a. b. c. d. X= 15, 1-side = 88 X= 7 ½ , 1-side =73 X= 10, 1-side = 65

  7. Review QA # 5 E B A C D F • In the triangles below, AB=DE and BC=EF. What additional information would be enough to prove that triangle ABC and DEF are congruent? Side AC ~DF: SSS Angle <B~<E : SAS

  8. Review QA # 6 • In the figure below, • If JK = LM, what will prove that JKL and JML are congruent? b. If JM = KL, what will prove that JKL and JML are congruent? Angle <1 ~<4: SAS Side KL ~ JM: SSS J K 1 3 2 Angle <3 ~<2: SAS Side JK ~ LM: SSS 4 M L

  9. Review QA # 7 K J L M • In the figure below, KL = JM. What postulate or theorem could be used to prove triangle JKL =LMJ? Side Angle Side

  10. Review QA # 8 Warm Up # 5 √290 √65 √117 √208 • A right triangle has legs of lengths 6 and 9. What is the length of the hypotenuse? • A right triangle has legs of lengths 8 and 12. What is the length of the hypotenuse? • A right triangle has legs of lengths 4 and 7. What is the length of the hypotenuse? • A right triangle has legs of lengths 11 and 13. What is the length of the hypotenuse?

  11. Review QA # 9 • Each diagonal of a rhombus bisects two angles of the rhombus. • The diagonals of a rhombus are perpendicular. • If one diagonal of a parallelogram are perpendicular, then the parallelogram is a rhombus. • If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. • All sides are equal and it’s a parallelogram. • Which of the following statements would prove that ABCD is a rhombus? • What type of triangle is formed by the points A(2, 3), B(2, -3) and C(5, 0)? • What type of triangle is formed by the points A(–1, -1), B(2, -3) and C(5, 0)? • What type of triangle is formed by the points A(0, 5), B(2, 0) and C(0, 0)? Isosceles Scalene Right Triangle

  12. Bell Work • If we have a parallelogram EFGH. Which of the following statements would prove that EFGH is a rhombus? Draw a Parallelogram, then a rhombus. • What type of triangle is formed by the points A(2, 4), B(2, -4) and C(5, 0)? • What type of triangle is formed by the points A(–1, -1), B(1, -3) and C(5, 0)? • What type of triangle is formed by the points A(0, 5), B(4, 0) and C(0, 0)? • All sides are equal. Isosceles Scalene Right Triangle

  13. 5 25 26 ? ? ? 3 7 10 Review QA # 10 • A fence built around a field has the dimensions shown below. • What is the approximate length of the entire fence? a. b. c. c. ? = 24 , Perimeter= 60 b. ? = 24 , Perimeter= 56 • ? = 4 , • Perimeter= 12

  14. G 1 J F 3 2 5 4 H 6 K Review QA # 11 • What additional information will be sufficient to prove that triangle GFH and JFK are similar? Remember we just need 2 angle to be congruent to have 2 similar triangles. Angle <5 ~<1: AAA Angle <6 ~ <2: AAA

  15. Review QA # 12 N Y M X O Z In the triangle below, XY = MN and <X = < M. • Which additional information would be sufficient to prove that both triangle are congruent? • Which additional information would NOT be sufficient prove both triangle are congruent? 1)Side XZ~ MO: SAS Angle <Z~<O : Yes AAS <Y ~<N : ASA 2) Side YZ ~ NO: NO ASS

  16. Review QA # 13 • What values of x and y make quadrilateral EFGH a parallelogram? Hint : Opposite sides are congruent. a.` b. 3x + 4y x – y E E F F 2 26 -x + 2y 4x + y 4 24 H H G G x = 4 y= 3 x = 6 y= 2

  17. Bell Work • What values of x and y make quadrilateral EFGH a parallelogram? Hint : Opposite sides are congruent. a. b. x + y 3x + 6 E E F F 9 11 2x + 3y x + 2y 7y 4 H H G G x = 5 y= 3 x = 3 y= 1

  18. Bell Work Warm Up # 5 √290 √65 √117 √208 • A right triangle has legs of lengths 6 and 9. What is the length of the hypotenuse? • A right triangle has legs of lengths 8 and 12. What is the length of the hypotenuse? • A right triangle has legs of lengths 4 and 7. What is the length of the hypotenuse? • A right triangle has legs of lengths 11 and 13. What is the length of the hypotenuse?

  19. Review QA # 14 If EFGH is a rhombus, solve for z? a. b. (x, y) (3, 4) E E F F (3+z, 4) (x+z, y) H H (z,0) (z,0) (0,0) (0,0) G G a2 + b2 = c2 32 + 42 = z2 Z=5 a2 + b2 = c2 x2 + y2 = z2

  20. Review QA # 15 If EFGH is a rhombus, solve for z. Then find Slope for FH and EG. Then multiply FH and EG. a. What do you notice about FH and EG? (3, 4) E F (3+z, 4) • Z = 5 • FH = ½ EG=-2 • FH x EG = -1 • Perpendicular H (z,0) (0,0) G

  21. Bell Work If EFGH is a rhombus, solve for z. Then find Slope for FH and EG. Then multiply FH and EG. a. What do you notice about FH and EG? (5, 12) E F (5+z, 12) • Z = 13 • FH =2/3 EG=-1 ½ • FH x EG = -1 • Perpendicular H (z,0) (0,0) G

  22. Review QA # 16 Warm Up # 9 If EFGH is a parallelogram, what are the coordinates of point E? a. b. (?, ?) (?, ?) E E F F (y, z) (6, 4) H H (5,0) (x,0) (0,0) (0,0) G G (1, 4) x = 6 – 5 =1 y= 4 (y – x , z)

  23. Review QA # 17 Warm Up # 9B • Which of the following facts would prove that EFGH and LMNO are similar? Hint: What should the ratio be for FG/MO, HG/NO ? What should <H and <G be congruent to ? If we have 2 parallel lines would it help? Which two? 6 F E 115 105 L 2 M 1) FG/MO = 1/3, HG/NO = 1/3 ,so FG and HG has to be three times as long as MO and NO. 105 9 115 3 2) <H = <N and <G = <O. We would only need 1 more angle congruent to prove that they are similar. N O H G 3) If EF || HG , and LM || NO. Then we can get <G=<O and <H = <N.

  24. Bell work A • Which of the following is not an undefined term use in geometry? • Triangle b. point c. line d. plane • Which of the following statements represents deductive reasoning? • Using logic to draw conclusions based on accepted statements. • Recognizing pattern in weather, then making a prediction based upon that pattern. • Singing “Yankee Doodle Dandy” to yourself. • Clark Gable • Which of the following statements represents inductive reasoning? • Using logic to draw conclusions based on accepted statements. • Recognizing a pattern in weather, then making a prediction based upon that pattern. • Reciting a Dr. Seus phrase to your neighbor. • Elvis Grabac. A B

  25. Bell Work 6 < X < 14 • A triangle has side lengths of 4 and 10 inches. What is the possible length for the third side? • A triangle has side lengths of 3 and 7 inches. What is the possible length for the third side? • A triangle has side lengths of 6 and 19 inches. What is the possible length for the third side? • A right triangle has legs of lengths 4 and 7. What is the length of the hypotenuse? • A right triangle has legs of lengths 11 and 13. What is the length of the hypotenuse? 4 < X < 10 13 < X < 25 √65 √290

  26. 3 7 ? Bell Work • A triangle has sides with lengths of 3 and 7 inches. Which of the following could be the perimeter of the triangle? • A triangle has sides with lengths of 6 and 10 inches. Which of the following could be the perimeter of the triangle? 3. A triangle has sides with lengths of 10 and 17 inches. Which of the following could be the perimeter of the triangle? 4<X<10, Perimeter: 14<y<20 4<X<16, Perimeter: 20<y<32 7<X<27, Perimeter: 34<y<54

  27. Review QA # 18 Warm Up # 10 Page 227 • Make a segment AB. • Put the tip of the compass on point A. • Open the pencil(with compass) tip so that it extend past point B. Then Draw an Arc. • Without adjusting the width of the compass, place the tip on point B and draw an arc that intersects the first arc at point C. • Draw a line segment from point A to C and from point B to C.

  28. Review QA # 19 Warm Up # 10B Page 271 • On a triangle ABC. Put the tip of the compass on to point B. • Open the pencil (with compass) tip so that it touches segment AC. Draw an arc. Label the intersection on AC point K and on AB point M. • Without adjusting the width of the compass. Place the tip on point K and draw an arc. Same with point M. • Where both arc intersects call it point H. • Lastly, make segment BH and that is the altitude.

  29. Review QA # 20 Warm-Up 10 C: Page 545: Pythagorean Theorem Proof.: Not drawn to scale y = 12.5 z = 6 X = 6 x • Find the area for Triangle x. • Find the area for Triangle y. • Find the area for Triangle z. • Find the area of x , y , z. • Find area of the trapezoid. • Find sum for triangle x, y, z. • Does answer number 6 have the same answer as number 5? 22 y 4 5 3 5 4 3 z 4)Area = 24.5 5) Area = 24.5 6) Area = 24.5 #5 and 6 = 24.5

  30. Review QA # 21 Warm-Up 21: Page 545: Pythagorean Theorem Proof. 4) =kj + ½ m2 X = ½ kj y = ½ m2 z = ½ kj x • Find the area for Triangle x. • Find the area for Triangle y. • Find the area for Triangle z. • Find the area of x , y , z. • Find area of the trapezoid. • Find sum for triangle x, y, z. • What happens when the Answer of problem 5 is equal to Answer of problem 6? 22 y j m k m k j z 5) = ½(k+J)(k+j) 6) =kj + ½ m2 4) ½(k+J)(k+j) =kj + ½ m2 K2 + J2 = M2

  31. You can work on Making up your QA’s • Sit quietly and work. • Have your homework ready for me to stamp.

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