Question

Given: Parallelogram ABCD with diagonal AC drawn Prove: ABC = CDA

Answer 1

Step-by-step explanation:

Consider the following figure:

By hypothesis, we have a Parallelogram ABCD with diagonal AC.

Now, since opposite sides of a parallelogram are congruent, we have:

`BC\cong AD`

and

`AB\cong DC`

and by the reflexive Postulate of Congruency, we get:

`AC\cong CA`

Now, the Side-Side-Side Theorem states that if three sides of a triangle are equal to the corresponding sides of the other triangle, the two triangles are said to be congruent, we can conclude that:

`\Delta ABC\cong\Delta CDA`

Then, we can conclude that the correct answer is:

Answer:

Since opposite sides of a parallelogram are congruent, we have:

`BC\cong AD`

and

`AB\cong DC`

Now, by the reflexive Postulate of Congruency, we get:

`AC\cong CA`

then, by Side-Side-Side Theorem we can conclude that:

`\Delta ABC\cong\Delta CDA`