1. Triangle Theorems

2. Example: Isosceles Triangles

3. Example: Isosceles Triangles
Name a pair of unmarked congruent segments.
___
BC is opposite D and BD is opposite BCD, so BC  BD.
Answer: BC  BD

4. Example: Isosceles Triangles
Which statement correctly names two congruent angles?
A. PJM  PMJ
B. JMK  JKM
C. KJP  JKP
D. PML  PLK A B C D

5. Example: Isosceles Triangles
ALGEBRA Find the value of each variable.
mDFE = 60
4x – 8 = 60
4x = 68
x = 17
DF = FE
6y + 3 = 8y – 5
3 = 2y – 5
8 = 2y
4 = y

6. Example: Isosceles Triangles
Find the value of x and the measures of the unknown sides.
X = 5
QS = RS = QR = 25
X = 11
LN = MN = 29

7. Name two congruent segments if 1  2.B. C. D. A B C D

9. Example: Exterior Angle Theorem
Find the value of x and then
find the measure of both
angles.
mLOW + mOWL = mFLW
x + 32 = 2x – 48
32 = x – 48
80 = x
Answer: So, mFLW = 2(80) – 48 or 112.
and mF0W = 80

10. Example: Exterior Angle Theorem
Find the measure of each missing angle
m1 = 104
m2 = 76
m 3 = 42
m4 = 48
m5 = 49

11. Practice
Find the measure of each missing angle

12. Angle-Side Relationship

13. Angle-Side Relationship
You can list the angles and sides of a triangle from smallest to largest (or vice versa)
The smallest side is opposite the smallest angle
The longest side is opposite the largest angle

14. Angle-Side Relationship
List the angles of ΔABC in order from smallest to largest.
Answer: C, A, B

15. Angle-Side Relationship
List the sides of ΔRST in order from shortest to longest.
A. RS, RT, ST
B. RT, RS, ST
C. ST, RS, RT
D. RS, ST, RT A B C D

16. EX: 1
x=15

17. EX: 2
x+x+15+3x=180
5x+15=180
5x=165
x=33

18. EX: 3
x-22+3x+19+x-17=180
5x-20=180
5x=200
x=40

19. EX: 4
x=138+21
x=159

20. EX: 5
42+x=77
x=35

21. EX: 6
x-6+x=148
2x-6=148
2x=154
x=77

22. EX: 7
x+4+x+3=127
2x+7=127
2x=120
x=60

23. EX: 8 Find the value of x <1=180-27-58=95° <3=180-132=48°
<2= =37°
x=180-37=143°

24. EX: 9 <4=180-132-24=14° <2=180-93=87° <1=180-83-14=83°