Question

The figure below shows line t, which intersects segment AB:

Segment AB is intersected by line t. Point C is on line t.

In the image above, line t is a perpendicular bisector and angle 4 is congruent to angle 6. Write a paragraph to prove that point C is equidistant from points A and B. (10 points)

Answer 1

Explanation:

Given:

Line 't' is a perpendicular bisector of AB.

AD ≅ BD

∠4 ≅ ∠6

To prove:

AC = BC

Construction done:

Completed triangle ABC by joining AC and BC.

Since, AD ≅ BD [Given]

∠4 ≅ ∠6 [Given]

∠ADC ≅ ∠BDC [Supplementary angles of ∠4 and ∠6]

CD ≅ CD [Reflexive property]

ΔACD ≅ ΔBCD [SAS property of congruence]

AC ≅ BC [CPCTC]