Question

24
one of the angles of right triangle p measures 65°. one of the angles of right triangle q measures 35°. which one of the following statements is true?
a triangle p is similar to triangle q because the interior angles of the two triangles have the same measures.
b triangle p is not similar to triangle q because the interior angles of the two triangles do not have the same
c triangle p is similar to triangle q because the two triangles are both right triangles.
d there is not enough information to determine whether the two triangles are similar or not.

Explanation:

Step1: Find angles of Triangle P

A right triangle has one 90° angle. Given one angle is 65°, the third angle is $180^\circ - 90^\circ - 65^\circ = 25^\circ$. So angles of P: $90^\circ, 65^\circ, 25^\circ$.

Step2: Find angles of Triangle Q

Right triangle Q has one 90° angle. Given one angle is 35°, the third angle is $180^\circ - 90^\circ - 35^\circ = 55^\circ$. So angles of Q: $90^\circ, 35^\circ, 55^\circ$.

Step3: Compare angle sets

The angle measures of P and Q do not match, so they are not similar (similar triangles require all corresponding angles equal).

Answer:

B. Triangle P is not similar to triangle Q because the interior angles of the two triangles do not have the same