Question

1. what is the primary use of the sas similarity criterion?

a. to measure angles in triangles
b. to prove the similarity of triangles
c. to prove congruence of triangles
d. to find the area of triangles

1. given △xyz ~ △pqr, if ∠x = 70°, ∠p = 70°, and the ratios (\frac{xy}{pq}=\frac{xz}{pr}=2), which of the following is true?

a. the angles are not proportional
b. the triangles are similar with a scale factor of 2
c. only △pqr is larger than △xyz
d. the triangles are congruent

1. what is the first step in proving triangles similar using aa similarity?

a. find the area of the triangles
b. calculate the lengths of sides
c. determine if the triangles are congruent
d. identify two pairs of corresponding angles

Explanation:

1. The SAS (Side - Angle - Side) similarity criterion is used to prove that two triangles are similar by showing that two sides of one triangle are proportional to two sides of another triangle and the included angles are equal.
2. Given $\triangle XYZ\sim\triangle PQR$, $\angle X = 70^{\circ}$, $\angle P=70^{\circ}$, and $\frac{XY}{PQ}=\frac{XZ}{PR} = 2$, the triangles are similar with a scale factor of 2. Similar triangles have proportional sides and equal corresponding angles.
3. The AA (Angle - Angle) similarity criterion states that if two pairs of corresponding angles in two triangles are equal, then the triangles are similar. So the first step in proving triangles similar using AA similarity is to identify two pairs of corresponding angles.

Answer:

1. B. To prove the similarity of triangles
2. B. The triangles are similar with a scale factor of 2
3. D. Identify two pairs of corresponding angles