Lesson 10 Angle Measurement and Perpendicular Lines

    • Let’s measure all kinds of angles.

Warm-up Number Talk: Quotients

Find the value of each expression mentally.

Activity 1 Angles Here, There, Everywhere

Problem 1

Use a protractor to find the value of each angle measurement in degrees.

  1. acute angle
  2. obtuse angle
  3. acute angle
  4. obtuse angle

Problem 2

Use a protractor to measure the labeled angles in each figure.

  1. trapezoid with an angle labeled and the opposite angle labeled t
  2. diamond with the top angle labeled q and an adjacent angle labeled r
  3. intersecting lines forming vertical angles with the bottom angle labeled e having one of the lines line extended further to intersect with a straight line with the angle of intersection labeled f

Activity 2 A Folding Challenge

Tyler gave Lin a challenge: “Without using a protractor, draw four angles. All angles have their vertex at point .”

Lin folded the paper twice, making sure each fold goes through point . Then, she traced the creases.

point labeled P inside of square.

  1. Your teacher will give you a sheet of paper. Draw a point on it. Then, show how Lin might have met the challenge.

  2. When Lin folded the paper, the creases formed a pair of perpendicular lines. What do you think “perpendicular lines” mean?

  3. Use Lin’s method to create a new pair of perpendicular lines through the same point. Trace the creases with a different color. Be prepared to explain how you know the lines you created are perpendicular.

  4. Which shapes have sides that are perpendicular to one another?

    Mark the perpendicular sides. Be prepared to explain how you know the sides are perpendicular.

    image of 4 geometric shapes. A. 5 sided shape with the same side lengths and angles. B, rectangle. C, Right triangle. D, parallelogram.

Practice Problem

Problem 1

Which of these shapes have segments that are perpendicular to one another? Trace or circle the perpendicular segments.

image of 3 geometric shapes.