1. Pearson Unit 1 Topic 4: Congruent Triangles 4-7: Congruence in Overlapping Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

2. TEKS Focus:
(6)(B) Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side- Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions.
(1)(E) Create and use representations to organize, record, and communicate mathematical ideas.
(1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.
(1)(G) Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

3. You can sometimes use the congruent corresponding sides of one pair of triangles to prove another pair of triangles are congruent. This involves overlapping triangles.

4. Example 1:
What common angle do  ACD and ECB share?
It is C.

5. Example 2: AD AB

6. Example 3:
Identify any common sides or angles that DEH and DFG may share.
Only D.

7. Example 4:
In order for BC  DC, which two triangles must be congruent?
BCA and DCE

8. Example 5: Statement Reason 1. ACD  BDC 1. Given 2. DEB  AEC
2. Vertical Angle Theorem
3. A  B
3. CPCTC
4. AC  BD
4. CPCTC
5. DEB  AEC
5. AAS
6. CE  DE
6. CPCTC

9. Example 6: Statement Reason 1. PS  RS, 1. Given 2. PSQ  RSQ
3. QS  QS
3. Reflexive Property of Congruence
4. PSQ  RSQ
4. SAS
5. TQ  TQ
5. Reflexive Property of Congruence
6. SQP  SQR
6. CPCTC
7. QP  QR
7. CPCTC
8. QPT  QRT
8. SAS