Question

1. using a compass and straightedge only, construct a line parallel to line ( m ) through the point shown.

a) construction:
b) list your steps in order.

1. benny and danielle make the following construction below. all circles shown are congruent (same size).

a) danielle claims that the triangle formed in the center ( \triangle aed ) is an equilateral triangle. is she correct? justify your conclusion.
b) benny claims that the quadrilateral shown in the middle with vertices ( abcd ) is a square. is benny correct? justify your conclusion.

1. bisect the angle below using only construction tools. do not estimate. show constructions clearly

a) construction:
b) explain how you know the line created has perfectly bisected the angle

Explanation:

Answer:

4b) 1. Place compass on a point on line \(m\), draw arc intersecting \(m\) and passing near the given point. 2. Without changing compass width, place on the given point, draw congruent arc. 3. Measure distance between the two intersection points on \(m\)'s arc, transfer to the new arc, mark the point. 4. Draw line through given point and marked point.
5a) Yes, she is correct. All sides of \(\triangle AED\) are radii of congruent circles, so \(AE = ED = AD\), making it equilateral.
5b) Yes, Benny is correct. \(AB = BC = CD = DA\) (radii of congruent circles) and all angles are right angles, so \(ABCD\) is a square.
6b) The constructed line bisects the angle because the two triangles formed by the angle sides and construction arcs are congruent (SSS), so the angles formed are equal.