1. 4-3 Congruent triangles

2. Congruent Polygons We will use: CPCTC for congruent triangles (A LOT!)
Corresponding parts of congruent triangles are congruent CPCTC!!

3. Example
Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.
Angles:
Sides:
Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE = RTPSQ.

4. TWAP
The support beams on the fence form congruent triangles. In the figure ΔABC  ΔDEF, which of the following congruence statements correctly identifies corresponding angles or sides? A. B. C. D.

5. Example In the diagram, ΔITP  ΔNGO. Find the values of x and y.
<O= <P CPCTC
m<O = m<P
6y – 14 = 40
6y = 54
y = 9

6. Example 2 continued CPCTC NG = IT x – 2y = 7.5 x – 2(9) = 7.5 y = 9
Answer: x = 25.5, y = 9

7. TOO In the diagram, ΔFHJ = ΔHFG. Find the values of x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5

8. Third Angle Theorem

9. Example
Write a two-column proof.
Prove: ΔLMN  ΔPON

10. Example continued 1. Given 1. 2. LNM  PNO
Proof:
Statements Reasons
1. Given 1.
2. LNM  PNO
2. Vertical Angles Theorem
3. M  O
3. Third Angles Theorem
4. ΔLMN  ΔPON
4. CPCTC

11. Homework
Pg #9, 11,13-16, 18-20, 37, 43