Question

Refer to the figure at the right

Answer 1

If
`\overline{AC} \simeq \overline{AD}`, then
`ACD` is isosceles, and its base angles are congruent. So, angles
`ACD` and
`ADC` are congruent.

If
`\overline{BE} \simeq \overline{BC}`, then
`BCE` is isosceles, and its base angles are congruent. So, angles
`BCE` and
`BEC` are congruent.

In the third case,
`ABE` is isosceles, and the side adjacent to the congruent angles are congruent, so
`\overline{AB} \simeq \overline{AE}`

Similarly, in this case,
`CED` is isosceles, and the side adjacent to the congruent angles are congruent, so
`\overline{CD} \simeq \overline{CE}`