Question

1. if two triangles have one pair of congruent angles and the surrounding sides are in a ratio of 4, are the triangles similar? a. yes, by sss similarity b. no, they must have three pairs of congruent angles c. no, they must have two pairs of congruent angles d. yes, by sas similarity 14. what is the point where the medians of a triangle intersect? a. centroid b. orthocenter c. incenter d. circumcenter 15. what is the first step in proving triangles similar using aa similarity? a. determine if the triangles are congruent b. find the area of the triangles c. identify two pairs of corresponding angles d. calculate the lengths of sides

Explanation:

1. The Side - Angle - Side (SAS) similarity criterion states that if two triangles have one pair of congruent angles and the sides including those angles are proportional, the triangles are similar. Here, we have one pair of congruent angles and the surrounding sides in a ratio, so by SAS similarity, the triangles are similar.
2. The centroid is the point where the medians of a triangle intersect. A median of a triangle is a line segment joining a vertex to the mid - point of the opposite side.
3. The AA (Angle - Angle) similarity criterion for triangles requires that two pairs of corresponding angles are congruent. So the first step in proving triangles similar using AA similarity is to identify two pairs of corresponding angles.

Answer:

1. d. Yes, by SAS similarity
2. a. Centroid
3. c. Identify two pairs of corresponding angles