Exploring Midpoints and Bisectors in Geometry

The video tutorial covers Section 1.5, focusing on midpoints, segment bisectors, and angle bisectors. It provides definitions and formulas for these concepts, explains adjacent angles, and demonstrates how to apply the midpoint formula. The tutorial includes examples to illustrate the use of angle bisectors in solving geometry problems.

Which of the following is NOT one of the definitions you need to memorize?

• Angle Bisector

• Segment Bisector

• Adjacent Angles

• Midpoint

What is the definition of a midpoint?

• A ray that divides an angle into two congruent angles

• A line that intersects a segment at its midpoint

• Two angles that share a common vertex and side

• A point that divides a segment into two congruent segments

Which of the following can be a segment bisector?

• A segment

• All of the above

• A line

• A ray

What is the key characteristic of adjacent angles?

• They share a common vertex but not a common side

• They overlap each other

• They are always congruent

• They share a common vertex and side but have no interior points in common

What does an angle bisector do?

• Divides an angle into two adjacent angles that are congruent

• Divides a segment into two congruent segments

• Creates two non-adjacent angles

• Intersects a segment at its midpoint

What is the midpoint formula for a segment with endpoints (x1, y1) and (x2, y2)?

• ((x1 + x2) / 2, (y1 + y2) / 2)

• ((x1 - x2) / 2, (y1 - y2) / 2)

• ((x1 / x2) / 2, (y1 / y2) / 2)

• ((x1 * x2) / 2, (y1 * y2) / 2)

If the endpoints of a segment are (3, 5) and (-4, 0), what is the midpoint?

• (-1, 5)

• (-0.5, 5)

• (-1, 2.5)

• (-0.5, 2.5)

Given the midpoint (3, 4) and one endpoint (-3, -1), what is the other endpoint?

• (7, 9)

• (9, -7)

• (-7, 9)

• (9, 7)

If Ray JK bisects angle HJL and the measure of angle HJL is 42°, what is the measure of angle HJK?

• 84°

• 42°

• 63°

• 21°

If Ray MO bisects angle LMN and the measures of the two congruent angles are 3x - 20 and x + 10, what is the value of x?

• 10

• 15

• 25

• 20