# TRIANGLE CONGRUENCE POSTULATES WORKSHEET

1. In the diagram below, prove that ΔPQW ≅ ΔTSW.

2. In the diagram below, prove that ΔABC ≅ ΔFGH.

3. In the diagram below, prove that ΔAEB ≅ ΔDEC.

4. In the diagram below, prove that ΔABD ≅ ΔEBC

5. In the diagram below, prove that ΔEFG ≅ ΔJHG.

 StatementsPQ ≅ STPW ≅ TWQW ≅ SWΔPQW ≅ ΔTSW ReasonsGivenGivenGivenSSS Congruence Postulate

Because AB = 5 in triangle ABC and FG = 5 in triangle FGH,

AB ≅ FG

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

AC ≅ FH

Use the distance formula to find the lengths of BC and GH.

Length of BC :

BC = √[(x2 - x1)2 + (y2 - y1)2]

Substitute (x1y1) = B(-7, 0) and (x2y2) = C(-4, 5).

BC = √[(-4 + 7)2 + (5 - 0)2]

=  √[32 + 52]

√[9 + 25]

√34

Length of GH :

GH = √[(x2 - x1)2 + (y2 - y1)2]

Substitute (x1y1) = B(1, 2) and (x2y2) = C(6, 5).

GH = √[(6 - 1)2 + (5 - 2)2]

√[52 + 32]

√[25 + 9]

√34

Conclusion :

Because BC = √34 and GH = √34,

BC ≅ GH

All the three pairs of corresponding sides are congruent. By SSS congruence postulate,

ΔABC ≅ ΔFGH

 StatementsAE ≅ DE, BE ≅ CE∠1 ≅ ∠2ΔAEB ≅ ΔDEC ReasonsGivenVertical Angles TheoremSAS Congruence Postulate

 StatementsBD ≅ BCAD || EC∠D ≅ ∠C∠ABD ≅ ∠EBCΔABD ≅ ΔEBC ReasonsGivenGivenAlternate Interior Angles TheoremVertical Angles TheoremASA Congruence Postulate

 StatementsFE ≅ JH∠E ≅ ∠J∠EGF ≅ ∠JGHΔEFG ≅ ΔJHG ReasonsGivenGivenVertical Angles TheoremAAS Congruence Postulate

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