Question

a) only perpendicular bisectors
b) only angle bisectors
c) perpendicular lines and equal lengths
d) only parallel lines

1. construction accuracy

why are compass and straightedge constructions useful?

1. circle intersection

when two circles of equal radius intersect, and their centers are separated by a distance equal to the radius, how many intersection points are there?
a) 0
b) 1
c) 2
d) infinite

1. construction problem

given an angle ∠abc, construct an angle congruent to it at point d. describe your steps.

1. invalid construction

which of these is not a valid compass and straightedge construction move?
a) drawing a circle with any center and radius
b) drawing a line through two points
c) measuring an angle with numbers
d) finding the intersection of two lines

Explanation:

Question 13

Step1: Recall circle - intersection concept

Two circles of equal radius can intersect in different ways. When they intersect and their centers are separated by a distance less than twice the radius and greater than 0, they intersect at two points.

Step2: Analyze the situation

Since the circles have equal radius and are intersecting, they will cross each other at two distinct points.

Step1: Draw an arc in ∠ABC

With B as the center, draw an arc that intersects BA and BC at points E and F respectively.

Step2: Re - create the arc at point D

With D as the center and the same radius as in Step 1, draw an arc that intersects a ray (say DX) at point G.

Step3: Measure the chord length in ∠ABC

Use the compass to measure the length of the chord EF.

Step4: Mark the point on the new arc

With G as the center and the length of EF as the radius, draw an arc that intersects the previously - drawn arc at point H.

Step5: Draw the ray

Draw the ray DH. ∠GDH is congruent to ∠ABC.

Step1: Understand compass - straightedge construction rules

Compass and straightedge construction allows for drawing circles, lines, and finding intersections, but not measuring angles with numbers.

Step2: Analyze each option

A. Drawing a circle with a given center and radius is a valid construction. B. Drawing a line through two points is a valid construction. C. Measuring an angle with numbers is not a valid compass - straightedge construction (compass and straightedge can be used to construct congruent angles, but not measure them numerically). D. Finding the intersection of two lines is a valid construction.

Answer:

C. 2

Question 14