1. Lesson 4-2: Congruent Triangles

2. Lesson 4-2: Congruent Triangles
Congruent Figures
Congruent figures are two figures that have the same size and shape.
IF two figures are congruent THEN they have the same size and shape.
IF two figures have the same size and shape THEN they are congruent.
Two figures are congruent IF AND ONLY IF they have the same size and shape.
Lesson 4-2: Congruent Triangles

3. Congruent Triangles - CPCTC
Two triangles are congruent IFF their corresponding parts (angles and sides) are congruent.
CPCTC:
Corresponding Parts of Congruent Triangles are Congruent B C A S T R = │
Vertices of the 2 triangles correspond in the same order as the triangles are named. ≡
A ↔ R; B ↔ S; C ↔ T
Corresponding sides and angles of the two congruent triangles: │ = ≡
Lesson 4-2: Congruent Triangles

4. Lesson 4-2: Congruent Triangles
 Z B A C X Y Z =
 Y
 B  _____ ≡ │ ≡
 X │
 C  ______ =
Note:
∆ ZYX
∆ABC  ______
∆ABC  ∆XYZ
Lesson 4-2: Congruent Triangles

5. Lesson 4-2: Congruent Triangles
Example…………
When referring to congruent triangles (or polygons), we must name corresponding vertices in the same order. S U N R A Y R Y
SUN  RAY A N U
Also NUS  YAR
Also USN  ARY S
Lesson 4-2: Congruent Triangles

6. Lesson 4-2: Congruent Triangles
Example ………
If these polygons are congruent, how do you name them ? P O U N M E A T S R
Pentagon MONTA  Pentagon PERSU
Pentagon ATNOM  Pentagon USREP
Etc.
Lesson 4-2: Congruent Triangles

7. Lesson 4-2: Congruent Triangles
Example ………
Given ΔABC ≅ ΔXYZ , AB = 26, YZ = 30, XY = 4x + 2.
Find the value of x. B Y
Draw.
Label.
Get equation.
Solve.
4x+2 30 26 A C X Z
4x+2 = 26
4x = 24
x = 6
Lesson 4-2: Congruent Triangles

8. Lesson 4-2: Congruent Triangles
Example ………
Given ΔEFG ≅ ΔPQR , m∠E = 95 , m∠R = 32 , and m∠F = 4x +13.
Find the value of x. F Q
Draw.
Label.
Get equation.
Solve.
4x =180
4x+140=180
4x=40
x=10
4x+13 32 95 E G P R
Lesson 4-2: Congruent Triangles