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QuestionConstruct a 45∘45^{\circ} angle using one of the methods below. Choose A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. We have a straight edge (like a ruler) and a compass. . We know how to construct a ray, a line segment, a perpendicular bisector, and an angle bisector.
3. We understand that a 90∘90^{\circ} angle is a right angle and that bisecting an angle divides it into two equal parts.

STEP 2

The problem asks us to construct a 45∘45^{\circ} angle. To do this, we first need to construct a 90∘90^{\circ} angle. The easiest way to do this is to construct a perpendicular bisector on a line segment.

STEP 3

Once we have a 90∘90^{\circ} angle, we can construct a 45∘45^{\circ} angle by bisecting the 90∘90^{\circ} angle. This is because bisecting an angle divides it into two equal parts, and half of 90∘90^{\circ} is 45∘45^{\circ}.

STEP 4

Therefore, the correct answer is option A "Construct a ray and label the endpoint A. Use a compass to construct a 90∘90^{\circ} angle with vertex A. Then construct the angle bisector of one of the 90∘90^{\circ} angles to get two 45∘45^{\circ} angles."

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