1. 4-3: Congruent Triangles
Do NOW
2/18/ :14 AM
4-3: Congruent Triangles

2. 4-3: Congruent Triangles
Page 276
16)
13 3/4°
17)
90 – 2x°
18)
33.2°
19)
162°
20)
61°
21)
48°, 48°
22)
128°, 128°
23)
15°, 60°, 105°
26)
50°
29)
36°
30)
48°
31)
32)
42°
33)
120°, 360°
34)
37.5°
35)
18°
2/18/ :14 AM
4-3: Congruent Triangles

3. 4-3: Congruent Triangles
2/18/ :14 AM
4-3: Congruent Triangles

4. Section 4-3 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us
Congruent Triangles
Section 4-3
Geometry PreAP, Revised ©2013
2/18/ :14 AM
4-3: Congruent Triangles

5. 4-3: Congruent Triangles
Congruent Polygons
Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides.
Two polygons are congruent polygons if and only if their corresponding sides are congruent.
2/18/ :14 AM
4-3: Congruent Triangles

6. 4-3: Congruent Triangles
Example 1
Given: ∆PQR  ∆STW. Identify the congruent parts of 𝑷𝑸 and ∠𝑾
2/18/ :14 AM
4-3: Congruent Triangles

7. 4-3: Congruent Triangles
Example 2
Given: ∆ABC  ∆DBC. Find the value of x.
BCA and BCD are rt. s.
BCA  BCD
mBCA = mBCD
(2x – 16)° = 90°
2x = 106
2/18/ :14 AM
4-3: Congruent Triangles

8. 4-3: Congruent Triangles
Your Turn
Given: ∆ABC  ∆DBC. Solve for ∆DBC.
mABC + mBCA + mA = 180°
mABC + 90° ° = 180°
mABC = 180°
mABC = 40.7°
DBC  ABC
mDBC = mABC
2/18/ :14 AM
4-3: Congruent Triangles

9. 4-3: Congruent Triangles
Example 3
Given: YWX and YWZ are right angles. 𝒀𝑾 bisects XYZ. W is the midpoint of 𝑿𝒁 . 𝑿𝒀  𝒀𝒁 Prove: ∆XYW  ∆ZYW
Statements
Reasons
1) YWX and YWZ are rt. s. Given
2) YWX  YWZ Right Angle Theorem
3) YW bisects XYZ Given
4) XYW  ZYW Definition of bisector
5) W is midpoint of 𝑿𝒁 Given
6) 𝑿𝑾  𝒁𝑾 Definition of Midpoint
7) 𝒀𝑾  𝒀𝑾 Reflexive Property
8) X  Z Third s Theorem
9) 𝑿𝒀  𝒀𝒁 Given
10) ∆XYW  ∆ZYW Def. of  ∆
2/18/ :14 AM
4-3: Congruent Triangles

10. 4-3: Congruent Triangles
Example 4
Given: 𝑨𝑫 bisects with 𝑩𝑬 𝑨𝑫  𝑫𝑬 ; 𝑩𝑬 bisects 𝑨𝑫 . A  D . Prove: ∆ABC  ∆DEC
2/18/ :14 AM
4-3: Congruent Triangles

11. 4-3: Congruent Triangles
Your Turn
The diagonal bars across a gate give it support. Since the angle measures and the lengths of the corresponding sides are the same, the triangles are congruent. Given: PR and QT bisect each other. PQS  RTS, QP  RT Prove: ∆QPS  ∆TRS
2/18/ :14 AM
4-3: Congruent Triangles

12. 4-3: Congruent Triangles
Assignment
Page , 23-25, 31, 32
2/18/ :14 AM
4-3: Congruent Triangles