Anyone know the answer to this ?

Answer & Step-by-step explanation:

The first thing we must do is gather information about the two triangles. The problem says that the two triangles are ≅. This sign, ≅, means that the two triangles are congruent. Congruent means two things that have the same measurements and are equal in measure.

So, since we know this, we can conclude that AB≅PQ, BC≅QR, and CA≅RP.

In order to find the measurement of PM, we are going to use the Pythagorean Theorem to find the measurement of PR. Then, we are going to divide that number by 2 because M is the midpoint of PR. Midpoints divides the line segment into two equal parts.

a = 6

b = 8

Now, let's plug in these numbers.

(6)² + (8)² = c²

Simplify the exponents.

36 + 64 = c²

Add the numbers together.

100 = c²

Take the square root of 100 and c².

√100 = √c²

Simplify the square roots.

10 = c

Now, divide 10 by 2.

10 / 2 = 5

So, the measurement of PM is 5 cm.