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

2. Isosceles Triangle at least two sides have the same length
9 in
9 in
3 miles
3 miles
3 miles
4 in

3. Properties of an Isosceles Triangle1
Has at least 2 equal sides
Has 2 equal angles
Has 1 line of symmetry

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

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

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

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

8. Isosceles Triangle Conjecture If a triangle is isosceles, then base angles are congruent.
If then

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

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

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

12. <c & <d are base angles and are congruent
Find the missing angle measures.
Triangle sum = 180°
180 = 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. EFG is an equilateral triangle Therefore <E = <F = <G
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 = = 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:
36o a b c
45o d
Isosceles triangle
Two angles are equal
Equilateral triangle
all angles are equal
Right-angled triangle
a = 36o
c = 180 ÷ 3 = 60o
d = 180 – ( )
= 45o
b = 180 – (2 × 36)
= 108o

19. Find the missing angle measures.
Kite - Made up of 2 isosceles triangles q
36o p s r
56o
p = 36o
q = 180 – (2 * 36) = 108o
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
b = 180 – (2 ×64o ) = 52o
h = i
c = d
e = f = g = 60o
h + i =
c + d =
h + i = 90
c + d = 108
h = i = 45o
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 = = 68.5o 2
e + 18 = a = 60
exterior angle = sum of remote interior angles
e = 60 – 18 = 42o

23. Find the missing angle measures.z
Find the value of x
Find the value of y
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. x 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