Prove that line AB ~= line AD.

Question

In the figure shown, <BAC ~= <DAC and <ACB ~= <ACD. Prove that line AB ~= line AD. (Hint: First show that triangle ABC ~= triangle ADC.) The image is a pryamid A is the piont at the top, the line to the right is B, exactly under A is C and then to the left it is D. ~~From book College Geometry A Problem-Solving Approach with Applications 2nd edition section 4.2 problem 34.

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Answer 1

Triangles ABC and ADC are similar because of the equal angles, also angles ADC and ABC are equal because ADC=180-(DAC+ACD) and ABC=180-(BAC+ACB). But side AC is common to both, so the triangles are congruent. That means corresponding sides have the same length. Therefore AB=AD.