Question

Write a paragraph proof.

Given: line BC is congruent to line EC and line AC is congruent to line ED
Prove: line BA is congruent to line ED

Answer 1

see the explanation

Explanation:

we know that

The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In this problem

Triangles ABC and DEC are congruent by SAS postulate

Because

BC≅EC

AC≅DC

and the include angle

m∠BCA≅m∠ECD ----> by vertical angles

Remember that

If two triangles are congruent, its corresponding sides and corresponding angles are congruent

therefore

BC≅EC

AC≅DC

and

BA≅ED