Question

Triangles wxz and xyz that share side xz with right angle xzw, wz equals 12, xz equals 6, and yz equals 3 since segment xz is perpendicular to segment wy, angles wzx and xzy are both right angles and congruent. The proportion 6 over 12 equals 3 over 6 shows the corresponding sides are proportional, so the triangles are similar by the SAS similarity postulate. Which of the following proportions is correct?

1) 6 over 12 equals 3 over 6
2) 6 over 3 equals 6 over 12
3) 6 over 6 equals 3 over 12
4) 12 over 6 equals 3 over 6

Answer 1

1) 6 over 12 equals 3 over 6. The correct proportion is 6 over 12 equals 3 over 6.

Step-by-step explanation:

The correct proportion is:

1) 6 over 12 equals 3 over 6

To determine if two triangles are similar, we can compare their corresponding sides. In this case, we have the proportion 6 over 12 (the length of the corresponding sides of triangle wxz) equals 3 over 6 (the length of the corresponding sides of triangle xyz).

By simplifying this proportion, we get 1 over 2 equals 1 over 2, which is true. Therefore, the triangles are similar.