# PROVING TRIANGLES ARE CONGRUENT WORKSHEET

Proving Triangles are Congruent Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on congruent triangles.

Before look at the worksheet, if you would like to learn triangle congruence postulates in detail,

## Proving Triangles are Congruent 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  ## Proving Triangles are Congruent 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 After having gone through the stuff given above, we hope that the students would have understood how to prove triangles are congruent.

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