Question

1. which of the following is used to prove that two triangles are similar using aa similarity? a. one pair of sides and one pair of angles b. two pairs of angles c. all angles and all sides d. three pairs of sides 35. if the measure of one intercepted arc in a circle is 140°, what is the measure of the other intercepted arc? a. 90° b. 220° c. 180° d. 140° 36. a circle with radius r1 = 10 is dilated to create a circle with radius r2 = 60. identify the scale factor (k). a. 5 b. 6 c. 3 d. 4

Explanation:

34.

The AA (Angle - Angle) similarity criterion states that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.

Step1: Recall circle - arc property

The sum of the measures of the intercepted arcs of a circle is 360°.

Step2: Calculate the other arc measure

Let the measure of one arc be \(a = 140^{\circ}\), and the measure of the other arc be \(b\). Then \(a + b=360^{\circ}\), so \(b = 360^{\circ}-140^{\circ}=220^{\circ}\).

Step1: Recall scale - factor formula

The scale factor \(k\) for a dilation of a circle (or any similar - figure dilation) is given by \(k=\frac{r_2}{r_1}\), where \(r_2\) is the radius of the dilated circle and \(r_1\) is the radius of the original circle.

Step2: Substitute values

Given \(r_1 = 10\) and \(r_2 = 60\), then \(k=\frac{60}{10}=6\).

Answer:

B. Two pairs of angles

35.