Question

3 from unit 1, lesson 5 this diagram is a straightedge and compass construction of the bisector of angle bac. only angle bac is given. explain the steps of the construction in order. include a step for each new circle, line, and point. 4 from unit 1, lesson 5 this diagram is a straightedge and compass construction of a line perpendicular to line ab passing through point c. which segment has the same length as segment ea? a ec b ed c be d bd

Explanation:

Step1: Bisecting angle BAC

1. Place the compass at point A. Draw an arc that intersects the two - sides of angle BAC at points B and C.
2. Without changing the compass width, place the compass at B and draw an arc. Then place the compass at C and draw another arc. Let these two arcs intersect at point D.
3. Draw the ray AD. Ray AD is the angle - bisector of angle BAC.

Step2: Perpendicular construction analysis

In the construction of a line perpendicular to line AB passing through point C, we use the property of circles. When constructing a perpendicular line, we create circles with equal radii. In this case, points A and C are centers of circles and E is a point of intersection of the circles. Since the circles are constructed with the same radius centered at A and C (in the perpendicular - line construction process), the length of segment EA is equal to the length of segment EC.

Answer:

1. Steps of angle - bisector construction:

• Place compass at A, draw arc intersecting sides of ∠BAC at B and C.
• With same compass width, draw arcs from B and C, intersect at D.
• Draw ray AD.

1. A. EC