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.

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]

Substitute (x₁, y₁) = B(-7, 0) and (x₂, y₂) = 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 (x₁, y₁) = B(1, 2) and (x₂, y₂) = 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

3. Answer :

4. Answer :

5. Answer :

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