Geometric Constructions: Angle Bisector and Perpendicular Lines Challenge

What are the four geometric constructions covered in this lesson?

• Bisecting an angle, constructing a perpendicular to a line through a point on the line, constructing a perpendicular to a line through a point not on the line, constructing a perpendicular bisector of a segment

• Drawing parallel lines, bisecting a segment, constructing a perpendicular to a line through a point on the line, constructing a perpendicular bisector of a segment

• Bisecting an angle, drawing parallel lines, constructing a perpendicular to a line through a point on the line, constructing a perpendicular bisector of a segment

• Drawing parallel lines, bisecting an angle, constructing a perpendicular to a line through a point not on the line, constructing a perpendicular bisector of a segment

What is the first step in bisecting an angle?

• Constructing a circle

• Drawing a perpendicular line

• Drawing two rays that intersect at a vertex

• Measuring the angle with a protractor

Why are segments AB and AC congruent in the angle bisector construction?

• They are both parallel

• They are both equal in length

• They are both radii of the same circle

• They are both perpendicular

What is the key concept in constructing a perpendicular to a line through a point on that line?

• Using a protractor

• Measuring the distance

• Drawing a circle

• Bisecting a 180-degree angle

Why must the arcs intersect at a point when constructing a perpendicular to a line through a point on that line?

• To ensure the perpendicular line is accurate

• To find the midpoint

• To measure the angle

• To draw a circle

What is the first step in constructing a perpendicular to a line through a point not on that line?

• Measuring the distance

• Using a protractor

• Drawing a circle

• Drawing a line and a point not on the line

Why are segments AP and BP congruent in the construction of a perpendicular to a line through a point not on that line?

• They are equal in length

• They are perpendicular

• They are parallel

• They are radii of the same circle

What is the goal of constructing a perpendicular bisector of a segment?

• To draw a circle

• To measure the segment

• To draw a parallel line

• To draw a perpendicular line that bisects the segment at its midpoint

Why are segments AC, BC, AD, and BD congruent in the construction of a perpendicular bisector?

• They are radii of congruent circles

• They are perpendicular

• They are parallel

• They are equal in length

What type of quadrilateral is formed when all sides are congruent in the perpendicular bisector construction?

• Parallelogram

• Rhombus

• Square

• Rectangle