Question

3 from unit 1, lesson 14
three line segments form the letter z.

rotate the letter z counterclockwise around the midpoint of segment bc by 180°.
describe the result.

4 from unit 1, lesson 14
there is a square, abcd, inscribed in a circle with center o. what is the smallest angle we
can rotate around o so that the image of a is b?
a 45°
b 60°
c 90°
d 180°

Explanation:

Step1: Analyze the position of points in a square inscribed in a circle

In a square \(ABCD\) inscribed in a circle with center \(O\), the central angles between adjacent vertices are equal. The total central angle around a point is \(360^{\circ}\).

Step2: Calculate the central angle between \(A\) and \(B\)

Since a square has \(4\) equal - length sides, the central angle \(\angle AOB=\frac{360^{\circ}}{4}\) (because the \(4\) central angles \(\angle AOB\), \(\angle BOC\), \(\angle COD\), \(\angle DOA\) are congruent).

$$ \angle AOB = 90^{\circ} $$

Answer:

C. \(90^{\circ}\)