Question

BRAINLIEST AND 30 POINTS FOR WHOEVER CAN EXPLAIN HOW TO GET THESE ANSWERS...

Answer 1

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 / MP

9 / CP = CP / 16

CP² = 144

CP = 12

Now, we can simply use Pythagorean theorem to find the other sides.

AC² = AP² + CP²

AC² = 9² + 12²

AC = 15

CM² = CP² + PM²

CM² = 12² + 16²

CM = 20