Q:

BRAINLIEST AND 30 POINTS FOR WHOEVER CAN EXPLAIN HOW TO GET THESE ANSWERS...Given: △ACM, m∠C=90°, CP⊥ AM. AP=9 cm, PM=16 cm. Explain how to get these answers: AC = 15, CM = 20, CP = 12

Accepted Solution

A:
Step-by-step explanation:Since m∠ACM = 90°, then by angle addition, m∠ACP + m∠PCM = 90°.Since CP⊥ AM, then by definition of perpendicular, m∠APC = 90°.  Since angles of a triangle add up to 180°, that means m∠PAC + m∠ACP = 90°.By substitution, m∠PCM = m∠PAC.Since m∠PCM + m∠CMP = 90°, then by substitution, m∠CMP = m∠PAC.Therefore, by AAA, △ACP and △CMP are similar.Having proven that the triangles are similar, we can write the proportion:AP / CP = CP / MP9 / CP = CP / 16CP² = 144CP = 12Now, we can simply use Pythagorean theorem to find the other sides.AC² = AP² + CP²AC² = 9² + 12²AC = 15CM² = CP² + PM²CM² = 12² + 16²CM = 20