Thread: △abc ≅ △dec

Given:

line segment AD bisects line segment BE
angle B ≅ angle E

Prove:

△ABC ≅ △DEC

See attachment for picture.

I need to do this using the statement versus reasons chart.

First step is the measure of segment BC is equal to the measure of segment CE. Why? Because a segment which is bisected has two parts with equal measures.

Second segment BC is congruent to segment CE. Why? Because two segments with equal measures are congruent.

Third angle ACB is congruent to angle DCE. Why? Because vertical angles are congruent.

Please look in your text for the exact wording of the theorems.

Can you finish the proof? If not I will help you further.

I can probably finish the proof in paragraph form but I need to do this using the statement versus reasons chart. Can you show me how?

As far as I know, that is what I did above.

Statement Reason
Measure of segment BC = measure of segment CE The two parts of a bisected segment have equal measures

Does that match the examples you were given? Please refer to your text for exact wording of the reasons (theorems and axioms)