PROVING TRIANGLES ARE CONGRUENT WORKSHEET

About "Proving triangles are congruent worksheet"

Proving Triangles are Congruent Worksheet :

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

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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 :

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 : 

Problem 4 : 

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

Problem 5 : 

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

After having gone through the stuff given above, we hope that the students would have understood, "Proving triangles are congruent worksheet". 

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