Question

Which triangle defined by three points on the coordinate plane is congruent with the triangle illustrated, and why?

A) (-1, 1)(-2, 1)(-1, 4); because corresponding pairs of angles are congruent.

B) (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of angles are congruent.

C) (-1, 1)(-2, 1)(-1, 4); because corresponding pairs of sides and corresponding pairs of angles are congruent.

D) (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of sides and corresponding pairs of angles are congruent

Answer 1

D) (-2, -3)(-4, -3)(-2, -9); because corresponding pairs of sides and corresponding pairs of angles are congruent

Explanation:

For triangles to be congruent, it is not enough that corresponding angles are congruent. In addition, there must be at least one pair of corresponding sides that are congruent. (Then all pairs will be congruent.)

The points listed in choices B and D are points that form a right triangle with leg lengths 2 and 6. However, choice B only refers to the angle measures, and not the sides. Choice D is the correct one.