4-4 Proving Triangles Congruent SSS, SAS

You proved triangles congruent using the definition of congruence.

• Use the SSS Postulate to test for triangle congruence.

• Use the SAS Postulate to test for triangle congruence.

Congruent Triangles

Do you really need six pairs of corresponding congruent parts to prove triangles congruent?

Look at the triangle. What angle is opposite side ST?What angle is included between RS and ST?

R S

T

Side-Side-Side Congruence Postulate (SSS)

If each of the three sides of one triangle are congruent to the side of another triangle, then the two triangles are congruent.

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Side-Angle-Side Congruence Postulate (SAS)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Angle-Side-Angle Congruence Postulate (ASA)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Use SSS to Prove Triangles Congruent

Prove: ΔQUD ΔADUGiven: QU AD, QD AU

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1.Given2.Given3.Reflexive4.SSS

Which information is missing from the flowproof?Given: AC AB

D is the midpoint of BC.Prove: ΔADC ΔADB

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A. AC AC

B. AB AB

C. AD AD

D. CB BC

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___ ___

___ ___

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Side-Angle-Side Congruence Postulate (SAA)If two angles and a side opposite one of them

in one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.

Use SAS to Prove Triangles are Congruent

ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG ΔHIG if EI FH, and G is the midpoint of both EI and FH.

3. Vertical Angles3. FGE HGI

2. Midpoint Theorem2.

Prove: ΔFEG ΔHIG

4. SAS4. ΔFEG ΔHIG

Given: EI FH; G is the midpoint of both EI and FH.

1. Given1.EI FH; G is the midpoint ofEI; G is the midpoint of FH.

ReasonsStatements

What are two short cuts to prove triangles congruent?

• Side-Side-Side (SSS)• Side-Angle-Side (SAS)

4-4 AssignmentPage 269, 5, 6, 12, 13, 16-19• Do all proof problems in two columns.• Write out the Given and Prove.• Draw the figure.