Parallel Lines and the Angle in a Triangle: IM 8.1.16
[url=https://im.kendallhunt.com/MS/teachers/3/1/16/preparation.html]“Parallel Lines and the Angles in a Triangle”[/url] from IM Grade 8 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 8.1.16
- IM 8.1.16 Lesson: Parallel Lines and the Angle in a Triangle
- Practice 8.1.16
- IM 8.1.16 Practice: Parallel Lines and the Angles in a Triangle
IM 8.1.16 Lesson: Parallel Lines and the Angle in a Triangle
Is each equation true or false?
[math]62-28=60-30[/math]
[math]3\cdot-8=(2\cdot-8)-8[/math]
[math]\frac{16}{-2}+\frac{24}{-2}=\frac{40}{-2}[/math]
Consider triangle ABC. Select the Midpoint tool and click on two points or a segment to find the midpoint.
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Rotate triangle [math]ABC[/math] [math]180°[/math] around the midpoint of side [math]AC[/math]. Right click on the point and select Rename to label the new vertex [math]D[/math].[br][br]Rotate triangle [math]ABC[/math] [math]180°[/math] around the midpoint of side [math]AB[/math]. Right click on the point and select Rename to label the new vertex [math]E[/math].[br][br]Look at angles [math]EAB[/math], [math]BAC[/math], and [math]CAD[/math]. 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 [math]EAB[/math] equal to the measure of any angle in triangle [math]ABC[/math]? If so, which one? If not, how do you know?
Is the measure of angle [math]CAD[/math] equal to the measure of any angle in triangle [math]ABC[/math]? If so, which one? If not, how do you know?
What is the sum of the measures of angles [math]ABC[/math], [math]BAC[/math], and [math]ACB[/math]?
Here is triangle △ABC. Line DE is parallel to line AC.
What is [math]m\angle DBA+b+m\angle CBE[/math]? Explain how you know.
[size=150][size=100]Use your answer to explain why [math]a+b+c=180.[/math][/size][/size]
Explain why your argument will work for [i]any[/i] triangle: that is, explain why the sum of the angle measures in [i]any[/i] triangle is [math]180°[/math].
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.
IM 8.1.16 Practice: Parallel Lines and the Angles in a Triangle
For each triangle, find the measure of the missing angle.
[size=150]Is there a triangle with two right angles? Explain your reasoning.[/size]
In this diagram, lines AB and CD are parallel.
[size=150]Angle [math]ABC[/math] measures [math]35^\circ[/math] and angle [math]BAC[/math] measures [math]115^\circ[/math].[br][br][size=100]What is [math]m\angle ACE?[/math][/size][/size]
What is [math]m\angle ACB?[/math]
What is [math]m\angle ACB?[/math]
Here is a diagram of triangle DEF.
Find the measures of angles [math]q[/math], [math]r[/math], and [math]s[/math].
Find the sum of the measures of angles [math]q[/math], [math]r[/math], and [math]s[/math].
What do you notice about these three angles?
The two figures are congruent. Label the points A',B' and C' that correspond to A, B, and C in the figure on the right.
If segment [math]AB[/math] measures 2 cm, how long is segment [math]A'B'[/math]? Explain.
The point [math]D[/math] is shown in addition to [math]A[/math] and [math]C[/math]. How can you find the point [math]D'[/math] that corresponds to [math]D[/math]? Explain your reasoning.