Lesson 16
Parallel Lines and the Angles in a Triangle
Let’s see why the angles in a triangle add to 180 degrees.
Problem 1
For each triangle, find the measure of the missing angle.
![Four triangles.](https://cms-im.s3.amazonaws.com/cxCfbk25uGJ5T9DEnLWTgxpJ?response-content-disposition=inline%3B%20filename%3D%228-8.1.D.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240907%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240907T232420Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3702ff7735c99314745d3a40baad5db86131d93738c54d421f1119d418e2f737)
Problem 2
Is there a triangle with two right angles? Explain your reasoning.
Problem 3
In this diagram, lines \(AB\) and \(CD\) are parallel.
![Four lines. Line A B. Line A C. Line C B. Line E D. Point C lies on line E D.](https://cms-im.s3.amazonaws.com/FiWnQDRFbdEQsp5YxGh4hU1q?response-content-disposition=inline%3B%20filename%3D%228-8.1.D.PP.Image.09.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D.PP.Image.09.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240907%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240907T232420Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0965d231d44255a404cdeaafd241fae9066d3ae9f9242c4eb213f9263340e6a0)
Angle \(ABC\) measures \(35^\circ\) and angle \(BAC\) measures \(115^\circ\).
- What is \(m{\angle ACE}\)?
- What is \(m{\angle DCB}\)?
- What is \(m{\angle ACB}\)?
Problem 4
Here is a diagram of triangle \(DEF\).
- Find the measures of angles \(q\), \(r\), and \(s\).
- Find the sum of the measures of angles \(q\), \(r\), and \(s\).
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What do you notice about these three angles?
![Three lines intersect to form Triangle D E F.](https://cms-im.s3.amazonaws.com/v2Se33sPEhpai8V1KLJ1XNKg?response-content-disposition=inline%3B%20filename%3D%228-8.1.D.PP.Image.07.6.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D.PP.Image.07.6.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240907%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240907T232420Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4b2654b9d2008645a5cfa96b72e45b734143f76669d7913e9c4b13109e482a22)
Problem 5
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 \(AB\) measures 2 cm, how long is segment \(A’B’\)? Explain.
- The point \(D\) is shown in addition to \(A\) and \(C\). How can you find the point \(D’\) that corresponds to \(D\)? Explain your reasoning.