1. Do the Daily Quiz
Warm Up on desk

2. 5.1
ESSENTIAL QUESTION
How do you identify congruent triangles and its corresponding parts?

3. VOCABULARY
When two triangles have exactly the same size and shape, the sides and angles that are the same in the triangles are called corresponding parts.
When all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent in two figures, the figures are congruent.

4. Given that JKL  RST, list All corresponding congruent parts.
Example 1
List Corresponding Parts
Given that JKL  RST, list
All corresponding
congruent parts.
SOLUTION
Which angles and sides
correspond to each other?
Corresponding Angles
∆JKL  ∆RST, so J  R.
Corresponding Sides
∆JKL  ∆RST, so JK  RS.
∆JKL  ∆RST, so K  S.
∆JKL  ∆RST, so KL  ST.
∆JKL  ∆RST, so L  T.
∆JKL  ∆RST, so JL  RT. 4

5. The two triangles are congruent.
Example 2
Write a Congruence Statement
The two triangles are congruent. a.
Identify all corresponding
congruent parts. b.
Write a congruence statement.
SOLUTION a.
Corresponding Angles
A  F
Corresponding Sides
AB  FD
B  D
BC  DE
C  E
AC  FE 5

7. In the diagram, PQR  XYZ.
Example 3
Use Properties of Congruent Triangles
In the diagram, PQR  XYZ.
Find the length of XZ.
Find mQ. a. b.
SOLUTION a.
Because XZ  PR, you know that XZ = PR = 10. b.
Because Q  Y, you know that mQ = mY = 95°. 7

8. Given STU  YXZ, list all corresponding congruent parts.
Checkpoint
Name Corresponding Parts and Congruent Triangles
Given STU  YXZ, list all corresponding congruent parts.
ANSWER
T  X; U  Z
ST  YX; TU  XZ;
SU  YZ; S  Y;

9. Which congruence statement is correct? Why?
Checkpoint
Name Corresponding Parts and Congruent Triangles
Which congruence statement is correct? Why? A.
JKL  MNP B.
JKL  NMP C.
JKL  NPM
ANSWER
B; This statement matches up the corresponding vertices in order.

10. Use the two triangles at the right.
Example 4
Determine Whether Triangles are Congruent
Use the two triangles at the right. a.
Identify all corresponding
congruent parts. E D F G
SOLUTION a.
Corresponding Angles
D  G
Corresponding Sides
DE  GE
DEF  GEF
DF  GF
DFE  GFE
EF  EF 10

11. Since, HJ  KJ, HG  KL, and JG  JL. (marked) So, HJG  KJL.
Example 5
Determine Whether Triangles are Congruent
In the figure, HG || LK. Determine whether the triangles are congruent. If so, write a congruence statement.
SOLUTION
HJG  KJL
Vertical angles are congruent.
H  K
Alternate Interior Angles Theorem
G  L
Alternate Interior Angles Theorem
Since, HJ  KJ, HG  KL, and JG  JL. (marked)
So, HJG  KJL. 11

12. yes; Sample answer: XVY  ZVW
Checkpoint
Determine Whether Triangles are Congruent 4.
In the figure, XY || ZW. Determine whether the two triangles are congruent. If they are, write a congruence statement.
ANSWER
yes; Sample answer: XVY  ZVW

13. Review

14. 1.
Name the smallest and largest angles of the triangle.
ANSWER

15. Name the shortest and longest sides of the triangle.2.
ANSWER 3.
ANSWER

16. Everett noticed that three streets in his town form a triangle
Everett noticed that three streets in his town form a triangle. He measured each distance and made this diagram. Are his measurements correct? Explain why or why not. 4.
ANSWER

17. Homework