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Given: angle B is congruent to angle D and segment AD is congruent to segment BC.Prove: triangle ABC is congruent triangle CDA

Given: angle B is congruent to angle D and segment AD is congruent to segment BC.Prove-example-1
User Kalimah
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1 Answer

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You have to prove that ΔABC and ΔCDA are congruent.

We know that ∠B and ∠D are congruent.

It is also given that AD=BC and since both segments are marked with an arrowhead, we also know that they are parallel AD||BC

Since segments AD||BC intersected by the transversal line AC, the angles formed have the following property:

∠DAC and ∠BCA are alternate interior angles, which means that they are congruent.

Line segments AC and CA are congruent by reflexive property

So,

∠B and ∠D are congruent, it is given.

∠DAC and ∠BCA are congruent because they are alternate interior angles.

Line segment AC and CA are congruent by reflexive property.

The triangles ΔABC and ΔCDA are congruent by AAS

Given: angle B is congruent to angle D and segment AD is congruent to segment BC.Prove-example-1
User Cililing
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