Question

in similar triangles, what is true about their corresponding sides? a. they are parallel b. they are proportional c. they are perpendicular d. they are equal in △def and △xyz, you find that ∠d = ∠x = 90° and ∠e = ∠y = 45°. what can you conclude about the triangles? a. the triangles are similar by aa similarity. b. the triangles are not similar. c. additional information is needed to conclude similarity. d. the triangles are congruent. how can you prove that two angles are congruent in coordinate geometry? a. by calculating the slopes of the sides forming the angles b. by measuring the lengths of the sides c. by using the distance formula d. by finding the area of the shapes

Explanation:

1. For the first question, by the definition of similar - triangles, the corresponding sides of similar triangles are proportional.
2. For the second question, since two pairs of corresponding angles ($\angle D=\angle X = 90^{\circ}$ and $\angle E=\angle Y = 45^{\circ}$) are equal, the triangles are similar by the AA (angle - angle) similarity criterion.
3. For the third question, in coordinate geometry, the slopes of the sides forming the angles can be used to prove angle congruence. If the angles have the same relationship between the slopes of their corresponding sides, they can be shown to be congruent.

Answer:

1. b. They are proportional
2. a. The triangles are similar by AA similarity.
3. a. By calculating the slopes of the sides forming the angles