1 / 18

Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ . 2. A part of a line that starts at one point and extends forever in one direction is called a _______.

sonya-foley
Download Presentation

Warm Up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ . 2. A part of a line that starts at one point and extends forever in one direction is called a _______. 3. Angles whose measures have a sum of 180° are ______________. 4. A part of a line between two points is called a ____________. complementary ray supplementary segment

  3. California Standards Review of Grade 6 MG2.2 Use properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Also covered: 6MG2.1

  4. So m1 = m3, or 1 3. Additional Example 1: Finding Angle Measures Use the diagram to find each angle measure. A. If m1 = 37°, find m3. 1 and 2 are supplementary. m2 = 180° – 37° = 143° The measures of 2 and 3 are supplementary. m3 = 180° – 143° = 37°

  5. Writing Math ~ The symbol for congruence is =, which is read as “is congruent to.”

  6. So m4 = m2, or 4 2. Additional Example 1: Finding Angle Measures Use the diagram to find each angle measure. B. If m4 = y°, find m2. 3 and 4 are supplementary. m3 = 180° – y° 2 and 3 are supplementary. m2 = 180° – m3 Substitute 180o – yo for m3. = 180° – (180o – yo) Distributive Property = 180° – 180° + y° = y° Simplify.

  7. 3 2 4 1 So m1 = m3, or 1 3. Check It Out! Example 1 Use the diagram to find each angle measure. A. If m1 = 42°, find m3. The measures of 1 and 2 are supplementary. m2 = 180° – 42° = 138° The measures of 2 and 3 are supplementary. m3 = 180° – 138° = 42°

  8. 3 2 4 1 So m4 = m2, or 4 2. Check It Out! Example 1 Use the diagram to find each angle measure. B. If m4 = x°, find m2. 3 and 4 are supplementary. m3 = 180° – x° 2 and 3 are supplementary. m2 = 180° – m3 Substitute 180o – xo for m3. = 180° – (180o – xo) Distributive Property = 180° – 180° + x° = x° Simplify.

  9. The angles in Example 1 are examples of adjacent angles and vertical angles. These angles have special relationships because of their positions. Adjacent angles have a common vertex and a common side, but no common interior points. Vertical angles are the nonadjacent angles formed by two intersecting lines.

  10. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angle pairs with special properties.

  11. Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. A. 4 Corresponding angles are congruent. m4 = 124°

  12. –124° –124° Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. B. 2 2 is supplementary to the 124° angle. m2 + 124° = 180° Subtract. m2 = 56° Simplify.

  13. Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. 2 and 6 are corresponding angles. C. 6 m6 = 56°

  14. 144° 1 m 4 3 6 5 n 8 7 Check It Out! Example 2 In the figure, line l|| line m. Find the measure of the angle. Alternate exterior angles are congruent. A. 7 m7 = 144°

  15. 144° 1 m 4 3 6 5 n 8 7 –144° –144° Check It Out! Example 2 In the figure, line l|| line m. Find the measure of the angle. B. 1 1 is supplementary to the 144° angle. m1 + 144° = 180° m1 = 36°

  16. 144° 1 m 4 3 6 5 n 8 7 Check It Out! Example 2 In the figure, line l|| line m. Find the measure of the angle. C. 6 Corresponding angles are congruent. m6 = 144°

  17. Lesson Quiz In the figure, line a || line b. 1. Name all angles congruent to 3. 1, 5, 7 2. Name all the angles supplementary to 6. 1, 3, 5, 7 3. If m1 = 105° what is m3? 105° 4. If m5 = 120° what is m2? 60°

More Related