IM 8.1.16 Lesson: Parallel Lines and the Angle in a Triangle

Author:
GeoGebra Classroom Activities, IM 6 - 8 Math, LearnZillion, Anthony OR 柯志明

Is each equation true or false?

Select all that apply
  • A
  • B
Check my answer (3)

Select all that apply
  • A
  • B
Check my answer (3)

Select all that apply
  • A
  • B
Check my answer (3)

Consider triangle ABC. Select the Midpoint tool and click on two points or a segment to find the midpoint.

Rotate triangle around the midpoint of side . Right click on the point and select Rename to label the new vertex . Rotate triangle around the midpoint of side . Right click on the point and select Rename to label the new vertex . Look at angles , ,  and . Without measuring, write what you think is the sum of the measures of these angles. Explain or show your reasoning.

Is the measure of angle equal to the measure of any angle in triangle ? If so, which one? If not, how do you know?

Is the measure of angle equal to the measure of any angle in triangle ? If so, which one? If not, how do you know?

What is the sum of the measures of angles , , and ?

Here is triangle △ABC. Line DE is parallel to line AC.

What is ? Explain how you know.

Use your answer to explain why

Explain why your argument will work for any triangle: that is, explain why the sum of the angle measures in any triangle is .

Create a few quadrilaterals. Use a protractor to measure the four angles inside the quadrilateral. What is the sum of these four angle measures?

What is the sum of these four angle measures?

Come up with an explanation for why anything you notice must be true (hint: draw one diagonal in each quadrilateral).

This diagram shows a square BDFH that has been made by images of triangle ABC under rigid transformations. Given that angle BAC measures 53 degrees, find as many other angle measures as you can.

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