1. Find m1.
A. 115
B. 105
C. 75
D. 65
5-Minute Check 1

2. Find m2.
A. 75
B. 72
C. 57
D. 40
5-Minute Check 2

3. Find m3.
A. 75
B. 72
C. 57
D. 40
5-Minute Check 3

4. Find m4.
A. 18
B. 28
C. 50
D. 75
5-Minute Check 4

5. Find m5.
A. 70
B. 90
C. 122
D. 140
5-Minute Check 5

6. Use properties of isosceles triangles.
Use properties of equilateral triangles.
Then/Now

7. legs of an isosceles triangle vertex angle base angles
Vocabulary

8. Concept

9. A. Name two unmarked congruent angles.
Congruent Segments and Angles
A. Name two unmarked congruent angles.
BCA is opposite BA and A is opposite BC, so BCA  A.
___
Answer: BCA and A
Example 1

10. B. Name two unmarked congruent segments.
Congruent Segments and Angles
B. Name two unmarked congruent segments.
___
BC is opposite D and BD is opposite BCD, so BC  BD.
Answer: BC  BD
Example 1

11. A. Which statement correctly names two congruent angles?
A. PJM  PMJ
B. JMK  JKM
C. KJP  JKP
D. PML  PLK
Example 1a

12. B. Which statement correctly names two congruent segments?
A. JP  PL
B. PM  PJ
C. JK  MK
D. PM  PK
Example 1b

15. Concept

16. Subtract 60 from each side. Answer: mR = 60 Divide each side by 2.
Find Missing Measures
A. Find mR.
Since QP = QR, QP  QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR.
Triangle Sum Theorem
mQ = 60, mP = mR
Simplify.
Subtract 60 from each side.
Answer: mR = 60
Divide each side by 2.
Example 2

17. Find Missing Measures
B. Find PR.
Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution.
Answer: PR = 5 cm
Example 2

18. ALGEBRA Find the value of each variable.
Find Missing Values
ALGEBRA Find the value of each variable.
Since E = F, DE  FE by the Converse of the Isosceles Triangle Theorem. DF  FE, so all of the sides of the triangle are congruent. The triangle is equilateral. Each angle of an equilateral triangle measures 60°.
Example 3

19. mDFE = 60 Definition of equilateral triangle 4x – 8 = 60 Substitution
Find Missing Values
mDFE = 60 Definition of equilateral triangle
4x – 8 = 60 Substitution
4x = 68 Add 8 to each side.
x = 17 Divide each side by 4.
The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.
DF = FE Definition of equilateral triangle
6y + 3 = 8y – 5 Substitution
3 = 2y – 5 Subtract 6y from each side.
8 = 2y Add 5 to each side.
Example 3

20. 4 = y Divide each side by 2. Answer: x = 17, y = 4 Find Missing Values
Example 3

21. Find the value of each variable.
A. x = 20, y = 8
B. x = 20, y = 7
C. x = 30, y = 8
D. x = 30, y = 7
Example 3