Given: AB=CB,
CD = ED
Prove: Line AB is parallel to line DE
(Please explain)

• Draw the two triangles so the two triangles share point C. It should look like a bowtie.

(1) AB is parallel to DE...

Given

(2) Angle A = Angle D If two parallel lines are cut by a transversal, alternate interior angles are equal.

(3) Angle BCA = Angle DCE Vertical angles are equal.

(4) Triangle BAC is similar to Triangle DEC ..

If 3 angles in one triangle are equal to three angles in another triangle, the triangles are similar.

(5) AB/DE = AC/EC

If two triangles are similar, corresponding sides are proportional...

• Hence , We prooved Line AB is parallel to line DE

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all it means is function 3