Question

Given: CP is perpendicular to AB, CP bisects AB, Prove: CA=CB

Answer 1

Proved CA=CB

Explanation:

Given,

In ΔABC, CP is perpendicular to AB.

And CP bisects AB.

So, AP=PB and ∠CPA=∠CPB=90°

The figure of the triangle is in the attachment.

Now, In ΔACP and ΔBCP.

AP = PB(given)

∠CPA = ∠CPB = 90°(perpendicular)

CP = CP(common)

So, By Side-Angle-Side congruence property;

ΔACP ≅ ΔBCP

According to the property of congruence;

"If two triangles are congruent to each other then their corresponding sides are also equal."

Therefore, CA = CB (corresponding side of congruent triangle)

CA = CB Hence Proved