Question

what is the first step in proving triangles similar using aa similarity?
a. calculate the lengths of sides
b. identify two pairs of corresponding angles
c. determine if the triangles are congruent
d. find the area of the triangles

in aa similarity, how many pairs of corresponding angles need to be congruent?
a. two
b. four
c. three
d. one

given δxyz - δabc, if xy = 10 cm, yz = 15 cm, and ab = 5 cm, what is the length of bc?
a. 15 cm
b. 5 cm
c. 7.5 cm
d. 10 cm

Explanation:

Step1: Understand AA similarity

AA (Angle - Angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. So the first step is to identify two pairs of corresponding angles.

Step2: Recall AA similarity angle count

By the AA similarity theorem, we need two pairs of congruent corresponding angles.

Step3: Use similarity ratio for side length

Since \(\triangle XYZ\sim\triangle ABC\), the ratio of corresponding sides is equal. That is \(\frac{XY}{AB}=\frac{YZ}{BC}\). Substitute \(XY = 10\mathrm{cm}\), \(AB = 5\mathrm{cm}\), \(YZ=15\mathrm{cm}\) into \(\frac{XY}{AB}=\frac{YZ}{BC}\), we get \(\frac{10}{5}=\frac{15}{BC}\). Cross - multiply: \(10\times BC=5\times15\), so \(BC=\frac{5\times15}{10}=7.5\mathrm{cm}\)

Answer:

1. B. Identify two pairs of corresponding angles
2. A. Two
3. C. \(7.5\mathrm{cm}\)