PROVING TRIANGLES ARE CONGRUENT WORKSHEET

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. 

Answers

1. Answer :

2. Answer :

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

3. Answer :

4. Answer :

5. Answer :

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.