1. 4.2 Properties of Isosceles Triangles
SWBAT classify triangles and apply the
HOMEWORK(?)
4.2

2. Warm-Up Name 2 pair of alternate interior angles
<5 & <3 and <4 & <1
2. What is the sum of m<1 + m<2 + m<3?
180°
If m<4 = 65° and m<5 = 50°, what is m<2?
65° 1 3 2 4 5
90°
40°
130°
50°
4. Find all the angle measures
50°
140°

3. 60º 90º 30º 60º 180º 30º 90º Review: Triangle Sum Theorem
The sum of all the angles equals 180º degrees.
60º
90º
30º +
60º
180º
30º
90º

4. Classification By Sides
Classification By Angles

5. Classifying Triangles
To classify, be as specific as possible. Classify by angle and then number of congruent sides
Obtuse,
Isosceles
Acute,
Scalene

6. Review: What is the missing angle?
70º
70º ? ? +
180º
70º
70º
180 – 140 = 40˚

7. Isosceles Triangle at least two sides are congruent
5 m
5 m
5 m
9 in
9 in
3 miles
3 miles
4 miles
4 in

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

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

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

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

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

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

14. Equilateral Triangle Triangle with all three sides are congruent
7 ft
7 ft
7 ft

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

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

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

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

19. 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°

20. 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 + 32 = 60
2x = 37
x = 18.5°

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

22. Find the missing angle measures.
Using the symbols categorize the the triangles and find the lettered angle.
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

23. 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
2r = 124
r = 62o

24. 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

25. 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°

26. 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°

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

28. Homework
4.2 Properties of Special Triangles