Question

1. which statement about similar circles is always true? a. their radii are equal. b. they have the same area. c. their diameters are equal. d. their corresponding radii are proportional. 2. what is the formula for converting degrees to radians? a. degrees = radians × 180/π b. radians = degrees × 180/π c. degrees = radians × π/180 d. radians = degrees × π/180 3. which postulate or theorem is typically used to establish triangle congruence before applying cpctc? a. sas postulate b. cpctc itself c. midpoint theorem d. pythagorean theorem

Explanation:

Step1: Recall definition of similar circles

Similar - shaped figures have proportional side - lengths. For circles, the radius is the key length. Similar circles have proportional radii. Radii being equal, same area, or equal diameters are properties of congruent circles. So for question 1, the answer is d.

Step2: Recall degree - radian conversion formula

The formula to convert degrees to radians is $Radians = Degrees\times\frac{\pi}{180}$. So for question 2, the answer is d.

Step3: Recall triangle congruence postulates and theorems

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used after proving triangles congruent. Mid - point theorem and Pythagorean theorem are not for proving triangle congruence directly. The SAS (Side - Angle - Side) postulate is used to prove triangle congruence before using CPCTC. So for question 3, the answer is a.

Answer:

1. d. Their corresponding radii are proportional.
2. d. Radians = Degrees × $\frac{\pi}{180}$
3. a. SAS Postulate