Pre-Algebra Chapter 3. Angles and Triangles
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1 Pre-Algebra Chapter 3 Angles and Triangles We will be doing this Chapter using a flipped classroom model. At home, you will be required to watch a video to complete your notes. In class the next day, we will work on the assignment for the section. To find the videos, go to trumanmath8.weebly.com and then find the Pre-Algebra page. Click on the appropriate Chapter and Section to find the video. Name Hour
2 3.1 Parallel Lines and Transversals Vocabulary: - Lines in the same plane that do not intersect. - Lines that intersect at right angles. - A line that intersects two or more lines Example 1: Use the figure to find the measures of (a) 1 and (b) 2. a) 1 and the 110 angle are corresponding angles. They are congruent. b) 1 and 2 are supplementary angles. On Your Own: Use the figure to find the measure of angle 1 and 2. Explain your reasoning.
3 Example 2: Use the figure to find the measures of all numbered angles. On Your Own: Use the figure to find the measures of all numbered angles. Explain your reasoning. Vocabulary: When two parallel lines are cut by a transversal, four are formed on the inside of the parallel lines and four are formed on the outside of the parallel lines.
4 Example 3: The photo shows a portion of an airport. Describe the relationship between each pair of angles. a) 3 and 6 b) 2 and 7 On Your Own: In Example 3, the measure of 4 is 84. Find the measure of the following angles. Explain your reasoning
5 3.2 Angles in Triangles Vocabulary: The angles inside a polygon are called. When the sides of a polygon are extended, other angles are formed. The angles outside the polygon that are adjacent to the interior angles are called. Example 1: Using interior angle measures. Find the value of x. Label all angle measures. On Your Own: Find the value of x. Label all angle measures.
6 Example 2: Finding exterior angle measures. Find the measure of the exterior angle. Label all angle measures. Example 3: Real Life Application: An airplane leaves from Miami and travels around the Bermuda Triangle. What is the value of x? Label all angle measures.
7 On Your Own Find the measure of the exterior angle. Label all angle measures. 5. In Example 3, the airplane leaves from Fort Lauderdale. The interior angle measure at Bermuda is The interior angle measure at San Juan is (x + 7.5). Find the value of x.
8 3.3 Angles of Polygons Vocabulary: A is a closed plane figure made up of three or more line segments that intersect only at their endpoints. A polygon is when every line segment connecting any two vertices lies entirely inside the polygon. A polygon is when at least one line segment connecting any two vertices lies outside the polygon. Polygon Names: 5 sides = 6 sides = 7 sides = 8 sides = 9 sides = 10 sides = n sides = Example 1: Finding the Sum of Interior Angle Measures Find the sum of the interior angle measures of the school crossing sign.
9 On Your Own: Find the sum of the interior angle measures of the marked polygon. Use the outside polygon of the spider web. Example 2: Finding an Interior Angle Measure of a Polygon Find the value of x. On Your Own: Find the value of x.
10 Vocabulary: In a, all the sides are congruent, and all the interior angles are congruent. Example 3: Real Life Application A cloud system discovered on Saturn is in the approximate shape of a regular hexagon. Find the measure of each interior angle of the hexagon. On Your Own Find the measure of each interior angle of the regular polygon.
11 Example 4: Find the measures of the exterior angles of each polygon. Label each angle with the angle measure. On Your Own: Find the measures of the exterior angles of the polygon. Label each angle with the angle measure.
12 3.4 Using Similar Triangles Example 1: Tell whether the triangles are similar.
13 Own Your Own: Tell whether the triangles are similar. Explain. Vocabulary: uses similar figures to find a missing measure when it is difficult to find directly. Example 2: Using Indirect Measurement You plan to cross a river and want to know how far it is to the other side. You take measurements on your side of the river and make the drawing shown. (a) Explain why ABC and DEC are similar. (b) What is the distance x across the river? On Your Own: WHAT IF The distance from vertex A to vertex B is 55 feet. What is the distance across the river?
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