Question

Can someone please fill out this chart I will really appreciate it

Answer 1

Explanation:

Given: i. AB||DE

ii. AC≅DC

Prove: ΔABC≅ΔDEC

From the two triangles, it can be observed that;

m<BAC≅m<EDC (alternate angles)

m<ABC≅m<DEC (alternate angles)

m<BCA≅m<ECD (vertically opposite angles)

m<BAC + m<ABC + m<BCA = m<EDC + m<DEC + m<ECD =
`180^(o)` (sum of angles in a triangle)

Since the three angles of the triangles are congruent respectively, then;

ΔABC≅ΔDEC (AAA congruence property)