Proving Points on a Perpendicular Bisector

EQ: Are points on a perpendicular bisector equidistant from the enpoints?

Assessment: Students will write a summary to prove the question

Directions

• 1) Use a compass to bisect each of the segments below.

• 2) Pick a point on the perpendicular bisector and mark it (this can be any point you want).

• 3) Draw a segment to connect each endpoint to the point you picked on the perpendicular bisector (this means that you are drawing two different segments).

• 4) Use a ruler to measure the length of each segment that you just drew.

• 5)Label both segments with the measurement.

Example shown:

Arc

Arc

Mark

Step 1 Demonstrated

Example shown:

Step 2 Demonstrated

Pick a point on the perpendicular

bisector and mark it

Example shown:Step 3

Demonstrated

Draw a segment to connect each

endpoint to the point you picked on the

perpendicular bisector

Example shown:

Step 4 Demonstrated

Use a ruler to measure the length of each segment that you just drew.

Example shown:

Step 5 Demonstrated

Use a ruler to measure the length of each segment that you just drew.

3.5 in 3.5 in

Answer the following questions:

• 1) What do you notice about the lengths of the segments connecting your point to the endpoints?

• 2) Fill in the blanks: Points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Solve for x and y

3x + 10 6x+34

2y 12

If the sides of the triangle are equidistant, then that means they are equal to each other.

Examine the Figure• If JL = 16, KM = 4x – 1, and KM is

a perpendicular bisector of JL determine which of the following values is/are correct. Select three that apply.

• A x = 3 • B JK = 11 • C KM = 15 • D KL = 17 • E perimeter of ΔKLM = 22 • F perimeter of ΔJKL = 50

Write your Summary

• All summaries MUST be at least 2-3 complete sentences. They should answer the essential question and summarize the notes

Homework

• Worksheet