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Side-Side-Side (SSS) Congruence Postulate

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Side-Side-Side (SSS) Congruence Postulate

All Three sides in one triangle are congruent to all three sides in the other triangle

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

(the angle is in between the 2 marked sides)

Share a side

Reason: reflexive property

Vertical Angles

Reason: Vertical Angles are congruent

1.BC || AD

3. BC AD

4. BD BD

Example 4: Proving Triangles Congruent

Given: BC║ AD, BC AD

Prove: ∆ABD ∆CDB

Statements

Reasons

1. Given

2. CBD ABD

2. Alt. Int. s Thm.

3. Given

4. Reflex. Prop. of

5.∆ABD ∆CDB

5. SAS Steps 3, 2, 4

2.QP bisects RQS

1. QR QS

4. QP QP

Check It Out! Example 4

Given: QP bisects RQS. QR QS

Prove: ∆RQP ∆SQP

Statements

Reasons

1. Given

2. Given

3. RQP SQP

3. Def. of bisector

4. Reflex. Prop. of

5.∆RQP ∆SQP

5. SAS Steps 1, 3, 4