# TRIANGLE CONGRUENCE POSTULATES WORKSHEET

## About "Triangle Congruence Postulates Worksheet"

Triangle Congruence Postulates Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on Triangle Congruence Postulates.

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## Triangle Congruence Postulates worksheet - Problems

Problem 1 :

In the diagram given below, prove that ΔPQW  ≅  ΔTSW

Problem 2 :

In the diagram given below, prove that ΔABC  ≅  ΔFGH

Problem 3 :

In the diagram given below, prove that ΔAEB  ≅  ΔDEC

Problem 4 :

In the diagram given below, prove that ΔABD  ≅  ΔEBC

Problem 5 :

In the diagram given below, prove that ΔEFG  ≅  ΔJHG

## Triangle Congruence Postulates worksheet - Solution

Problem 1 :

In the diagram given below, prove that ΔPQW  ≅  ΔTSW

Solution :

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

Problem 2 :

In the diagram given below, prove that ΔABC  ≅  ΔFGH

Solution :

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]

Here (x₁, y₁)  =  B(-7, 0) and (x₂, y₂)  =  C(-4, 5)

BC  =  √[(-4 + 7)² + (5 - 0)²]

BC  =  √[3² + 5²]

BC  =  √[9 + 25]

BC  =  √34

Length of GH :

GH  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

Here (x₁, y₁)  =  G(1, 2) and (x₂, y₂)  =  H(6, 5)

GH  =  √[(6 - 1)² + (5 - 2)²]

GH  =  √[5² + 3²]

GH  =  √[25 + 9]

GH  =  √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

Problem 3 :

In the diagram given below, prove that ΔAEB  ≅  ΔDEC

Solution :

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

Problem 4 :

In the diagram given below, prove that ΔABD  ≅  ΔEBC

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

Problem 5 :

In the diagram given below, prove that ΔEFG  ≅  ΔJHG

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

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