Question

Since segment xz is perpendicular to segment wy, angles wzx and xzy are both right angles and congruent. the proportion ________ shows the corresponding sides are proportional, so the triangles are similar by the sas similarity postulate. 5 over 10 equals 5 over 2 and one half 5 over 10 equals 5 over 5 10 over 5 equals 5 over 2 and one half 10 over 5 equals 2 and one half over 5

Answer 1

The question asks about the SAS similarity postulate for right triangles, looking for the proportion that shows proportional sides when segment xz is perpendicular to segment wy. The correct proportion indicating similar triangles is 5/10 = 2.5/5 or 1/2 = 1/2.

Step-by-step explanation:

The question refers to similar triangles and the conditions that must be met for two triangles to be considered similar by the SAS (Side-Angle-Side) similarity postulate.

In the context of similar right triangles where segment xz is perpendicular to segment wy, angles wzx and xzy are both right angles and thus congruent. The SAS similarity postulate states that if one angle of a triangle is equal to one angle of another triangle and the sides around the equal angles are proportional, then the triangles are similar.

The correct proportion to show that corresponding sides are proportional is 5/10 = 2.5/5, which simplifies to 1/2 = 1/2. This proves that the sides around the right angles are proportional, and, along with the fact that the triangles have congruent angles, satisfies the SAS postulate for triangle similarity.