Question

1. this diagram was constructed with straightedge and compass tools. f is the center of one circle, and g is the center of the other. select all line segments that must have the same length as segment fh. a. segment gh b. segment fh c. segment gj d. segment fj e. segment fg 8. kiran used a compass to make a circle with radius the same length as segment qr. he labeled the center w. which statement must be true? a. qr = wx b. qr < wx c. qr = wz d. wz > qr

Explanation:

Step1: Recall circle - radius property

In a circle, all radii have the same length.

Step2: Analyze problem 7

Since \(F\) is the center of one circle and \(FH\) is a radius of the circle with center \(F\), and \(G\) is the center of the other circle. Segments \(FH\), \(FJ\) are radii of the circle with center \(F\), and \(GH\), \(GJ\) are radii of the circle with center \(G\). All radii of a given circle are equal in length. So \(FH = FJ\) and \(GH=GJ\), but we are looking for segments equal to \(FH\), so \(FH = FJ\). Also, \(FH\) and \(GH\) are not necessarily equal (depends on the size of the circles). \(FG\) is the distance between the centers and is not a radius of either circle.

Step3: Analyze problem 8

Kiran made a circle with center \(W\) and radius equal to the length of segment \(QR\). In a circle, all radii are equal. \(WX\) and \(WZ\) are radii of the circle with center \(W\). Since the radius of the circle is equal to the length of \(QR\), we have \(QR = WX\) and \(QR = WZ\).

Answer:

1. D. segment \(FJ\)
2. A. \(QR = WX\), C. \(QR = WZ\)