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Lesson 4.2

Lesson 4.2. Discover the properties of Isosceles Triangles. HOMEWORK: Lesson 4.2/1-11 QUIZ Tomorrow: 4.1 – 4.2. Isosceles Triangle at least two sides have the same length. 5 m. 5 m. 5 m. 9 in. 9 in. 3 miles. 3 miles. 3 miles. 4 in. Properties of an Isosceles Triangle. 1.

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Lesson 4.2

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  1. Lesson 4.2 Discover the properties of Isosceles Triangles. HOMEWORK: Lesson 4.2/1-11 QUIZ Tomorrow: 4.1 – 4.2

  2. Isosceles Triangleat least two sides have the same length 5 m 5 m 5 m 9 in 9 in 3 miles 3 miles 3 miles 4 in

  3. Properties of an Isosceles Triangle 1 • Has at least 2 equal sides • Has 2 equal angles • Has 1 line of symmetry

  4. Equilateral TriangleIsosceles Triangle with all three sides are congruent 7 ft 7 ft 7 ft

  5. The vertex angle is the angle between two congruent sides Parts of an Isosceles Triangle:

  6. The base angles are the angles opposite the congruent sides Parts of an Isosceles Triangle:

  7. The base is the side opposite the vertex angle Parts of an Isosceles Triangle:

  8. Isosceles Triangle ConjectureIf a triangle is isosceles, thenbase angles are congruent. If then

  9. If then Converse of Isosceles Triangle ConjectureIf a triangle has two congruent angles, then it is an isosceles triangle.

  10. Equilateral Triangle Conjecture An equilateral triangle is equiangular, and an equiangular triangle is equilateral.

  11. b <68° and < a are base angles  therefore they are congruent Find the missing angle measures. ma = 68˚ Triangle sum to find <b m<b = 180 – 68 - 68 m<b = 180 -136 mb = 44˚ 68˚ a

  12. Find the missing angle measures. Triangle sum = 180° 180 = 119 + c + d 180 – 119 = c + d 61 = c + d <c & <d are base angles and are congruent <c = ½ (61) = 30.5 <d = ½ (61) = 30.5 mc = md = 30.5˚ 119˚ 30.5˚ c d

  13. Find the missing angle measures. E EFG is an equilateral triangle Therefore <E = <F = <G 180 /3 = 60 mE = mF = mG = 60˚ 60˚ G F 60˚

  14. Find the missing angle measures. Find mG. ∆GHJ is isosceles < G = < J x + 44 = 3x 44 = 2x x= 22 Thus m<G = 22 + 44 = 66° And m<J = 3(22) = 66°

  15. Find the missing angle measures. Find mN Base angles are = 6y = 8y – 16 -2y = -16 y= 8 Thus m<N = 6(8) =48°. m<P = 8(8) – 16 = 48°

  16. Find the missing angle measures. Using Properties of Equilateral Triangles Find the value of x. ∆LKM is equilateral. m<K = m<L = m<M 180/3 = 60° 2x + 23 = 60 2x = 37 x = 18.5°

  17. Find the missing side measures. Using Properties of Equilateral Triangles Find the value of y. ∆NPO is equiangular therefore, ∆NPO is also equilateral. ft ft 5y – 6 = 4y +12 y – 6 = 12 y = 18 Side NO = 5(18) – 6 = 90ft

  18. Find the missing angle measures. Using the symbols describing shapes answer the following questions: b 45o d a c 36o Equilateral triangle all angles are equal Isosceles triangle Two angles are equal Right-angled triangle c = 180 ÷ 3 = 60o a = 36o d = 180 – (45 + 90) = 45o b = 180 – (2 × 36) = 108o

  19. Find the missing angle measures. Kite - Made up of 2 isosceles triangles q 36o s p = 36o q = 180 – (2 * 36) = 108o p r 56o 56 + (r + s) = 180o (r + s) = 180 – 56 = 124 Because r = s r = s = 124 ÷ 2 = 62o

  20. Find the missing angle measures. a = 64o Equilateral triangle h = i b = 180 – (2 ×64o ) = 52o c = d e = f = g = 60o h + i = 180 - 90 h + i = 90 c + d = 180 - 72 h = i = 45o c + d = 108 c = d = 54o

  21. p = 50o q = 180 – (2 ×50o ) = 80o r = q = 80o vertical angles are equal Therefore: s = t = p = 50o

  22. Find the missing angle measures. Properties of Triangles p = q = r = 60o a = b= c = 60o d = 180 – 60 = 120o s = t = 180 - 43= 68.5o 2 e + 18 = a = 60 exterior angle = sum of remote interior angles e = 60 – 18 = 42o

  23. Find the missing angle measures. • Find the value of x • Find the value of y z • x is a base angle • 180 = x + x + 50 • 130 = 2x • x = 65° 2) y & z are remote interior angles and base angles of an isosceles triangle Therefore: y + z = x and y = z y + z = 80° y = 40°

  24. Find the missing angle measures. • Find the value of x • Find the value of y 1) ∆CDE is equilateral All angles = 60° Using Linear Pair <BCD = 70° x is the vertex angle x = 180 – 70 – 70 x = 40° 70° 60° 2) y is the vertex angle y = 180 – 100 y = 80°

  25. Find the missing measures. Lesson Quiz Find each angle measure. 1. mR 2. mP Find each value. 3.x4.y 5.x

  26. Find the missing angle measures. Lesson Quiz con’t 6. The vertex angle of an isosceles triangle measures (a + 15)°, and one of the base angles measures 7a°. Find a and each angle measure. (Make a sketch)

  27. Lesson Quiz Solutions • 28° • 124° • 20 • 6 • 26 a = 11; 26°; 77°; 77°

  28. Homework In your textbook: • Lesson 4.2/ 1-11

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