1 / 16

Notes 1.5 Angle Pair Relationships

Notes 1.5 Angle Pair Relationships. L.T. I can identify special angle pairs and use their relationships to find angle measures. A. Vertical Angles. 1. 2. 4. 3.

edward-saunders
Télécharger la présentation

Notes 1.5 Angle Pair Relationships

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. Notes 1.5Angle Pair Relationships L.T. I can identify special angle pairs and use their relationships to find angle measures.

  2. A. Vertical Angles 1 2 4 3 Previously, you learned that two angles are adjacent if they share a common vertex and side but have no common interior points. In this lesson, you will study other relationships between pairs of angles. Two angles are vertical anglesif their sides form two pairs of opposite rays. Vertical Angle Pairs are CONGRUENT 1 and 3 are vertical angles. 2 and 4 are vertical angles.

  3. B. Linear Pairs 5 6 Two adjacent angles are a linear pair if the form a straight line. 30° 150° Linear Angle Pairs add up to 180°. 5 and 6 are a linear pair.

  4. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No.

  5. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? Are 3 and 4 a linear pair? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No. Yes. The angles are adjacent and their noncommon sides are opposite rays.

  6. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? Are 3 and 4 a linear pair? Are 1 and 3 vertical angles? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No. Yes. The angles are adjacent and their noncommon sides are opposite rays. No. The sides of the angles do not form two pairs of opposite rays.

  7. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? Are 3 and 4 a linear pair? Are 1 and 3 vertical angles? Are 2 and 4 vertical angles? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No. Yes. The angles are adjacent and their noncommon sides are opposite rays. No. The sides of the angles do not form two pairs of opposite rays. The sides of the angles do not form two pairs of opposite rays. No.

  8. Finding Angle Measures 5 5 5 8 8 8 6 6 6 7 7 7 In the stair railing shown, 6 has a measure of 130˚. Find the measures of the other three angles. SOLUTION 6 and 8 are vertical angles. So, they are congruent and have the same measure. 50° m8 = m6 = 130˚ 6 and 7 are a linear pair. So, the sum of their measures is 180˚. 130° 130° 130° 130° m6 + m7 = 180˚ 50° 130˚ + m7 = 180˚ m7 = 50˚ 7 and 5 are vertical angles. So, they are congruent and have the same measure. All 4 angles together equal 360°

  9. C. Supplementary Angles Two angles are supplementary if the sumof their measures is 180 degrees. Each angle is the supplement of the other. 1 2 Supplementary Angle Pairs add up to 180°. These are supplements of each other because their angles add up to 180.

  10. Example 1 Find the value of x.

  11. Example 2 Find the value of x.

  12. D. Complementary Angles Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other. 1 Complementary Angle Pairs add up to 90°. 2 These are complements of each other because their angles add up to be 90.

  13. Example 1 Find the value of x.

  14. Example 2 Find the value of x.

  15. D. Angle Bisector An angle bisector is a ray that divides an angle into two congruent angles. It cuts the angle in half.

  16. Example 1 • QR bisects PQS;mPQS= 3x mSQR= 5x  20 Solve for x and find mPQR. Work it out on board

More Related