1. DRILL Prove each pair of triangles are congruent.
Given: PQ is congruent to QR and PS is congruent to SR.
Given: AB ║ CD,
BC ║ DA

2. Objectives: Use congruent triangles to plan and write proofs.
Use congruent triangles to prove constructions are valid.

3. 8.4 Using Triangle Congruence CPCTC

4. Corresponding parts
When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are congruent, that means that ALL the corresponding parts are congruent. A C B
That means that EG CB G E F
What is AC congruent to?
Segment FE

5. Corresponding parts of congruent triangles are congruent.

6. CPCTC Corresponding Parts of Congruent Triangles are Congruent.
You can only use CPCTC in a proof AFTER you have proved congruence.

7. Ex. Proof Given: A is the midpoint of MT, A is the midpoint of SR.
Prove: NS is congruent to TR.

8. Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR.
Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR.
Statements:
A is the midpoint of MT, A is the midpoint of SR.
MA ≅ TA, SA ≅ RA
MAS ≅ TAR
∆MAS ≅ ∆TAR
NS is congruent to TR
Reasons:
Given

9. Reasons: Statements: Given
Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR.
Reasons:
Given
Definition of a midpoint
Statements:
A is the midpoint of MT, A is the midpoint of SR.
MA ≅ TA, SA ≅ RA
MAS ≅ TAR
∆MAS ≅ ∆TAR
NS is congruent to TR

10. Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR.
Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR.
Statements:
A is the midpoint of MT, A is the midpoint of SR.
MA ≅ TA, SA ≅ RA
MAS ≅ TAR
∆MAS ≅ ∆TAR
NS is congruent to TR
Reasons:
Given
Definition of a midpoint
Vertical Angles Theorem

11. Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR.
Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR.
Statements:
A is the midpoint of MT, A is the midpoint of SR.
MA ≅ TA, SA ≅ RA
MAS ≅ TAR
∆MAS ≅ ∆TAR
NS is congruent to TR
Reasons:
Given
Definition of a midpoint
Vertical Angles Theorem
SAS Congruence Postulate

12. Statements: Reasons: A is the midpoint of MT, A is the midpoint of SR.
Given: A is the midpoint of MT, A is the midpoint of SR. Prove: NS is congruent to TR.
Statements:
A is the midpoint of MT, A is the midpoint of SR.
MA ≅ TA, SA ≅ RA
MAS ≅ TAR
∆MAS ≅ ∆TAR
NS is congruent to TR
Reasons:
Given
Definition of a midpoint
Vertical Angles Theorem
SAS Congruence Postulate
CPCTC

13. Ex. 2: Using more than one pair of triangles.
Given: 1≅2, 3≅4.
Prove ∆BCE≅∆DCE
Prove: segment DC is congruent to segment CD 2 4 3 1

14. Given: QSRP, segment PT≅ segment RT Prove: segment PS≅ segment RS4 3 1
Statements:
QS  RP
PT ≅ RT
Reasons:
Given

15. Homework
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