1 / 18

Angle Pair Relationships

Angle Pair Relationships. Section 1.5. Vocabulary. An angle consists of two different rays with the same endpoint . The rays are the sides of the angle. The endpoint is the vertex of the angle. Vocabulary. An angle is named with three points, just the vertex , or a number .

arvid
Download Presentation

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. Angle Pair Relationships Section 1.5

  2. Vocabulary An angle consists of two different rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle.

  3. Vocabulary An angle is named with three points, just the vertex, or a number. An angle can be named with just the vertex only if it is the only angle with that particular vertex. The vertex is always the middle point when naming an angle with three points.

  4. Vocabulary When naming an angle, always remember to put a symbol in front. Otherwise you are naming a point or plane. To denote the measure of an angle, we write an “m” in front of the angle sign: o

  5. Vocabulary An acute angle has a measure between 0o and 90o A right angle has a measure of 90o An obtuse angle has a measure between 90o and 180o A straight angle has a measure of 180o

  6. Vocabulary Two angle are congruent angles if they have the same measure. An angle bisector is a ray that divides an angle into two congruent angles.

  7. Vocabulary Two angles are complementary angles if the sum of their measures is 90o. Two angles are supplementary angles if the sum of their measures is 180o.

  8. Vocabulary Adjacent angles are two angles that share a common vertex and side, but have no common interior points.

  9. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. 1. Because 41° + 49° = 90°, FGK and GKLare complementary angles. Because 49° + 131° = 180°,HGKand GKL are supplementary angles. Because FGKand HGKshare a common vertex and side, theyare adjacent. for Example 1 GUIDED PRACTICE

  10. b. You can draw a diagram with supplementary adjacent angles to illustrate the relationship. m 3 = 180° – m 4 = 180° –56° = 124° b. Given that 3 is a supplement of 4and m 4=56°, find m3. EXAMPLE 2 Find measures of a complement and a supplement SOLUTION

  11. for Examples 2 and 3 GUIDED PRACTICE 5.LMNand PQRare complementary angles. Find the measures of the angles if m LMN= (4x –2)° and m PQR = (9x + 1)°.

  12. Vocabulary Two adjacent angles are a linear pair if their noncommon sides are opposite rays. The angles in a linear pair are supplementary angles.

  13. Vocabulary Two angles are vertical angles if their sides form two pairs of opposite rays. Vertical angles are congruent to each other.

  14. 1 and 4 are a linear pair. 4 and 5 are also a linear pair. Identify all of the linear pairs and all of the vertical angles in the figure at the right. ANSWER 1 and 5 are vertical angles. ANSWER EXAMPLE 4 Identify angle pairs SOLUTION To find vertical angles, look or angles formed by intersecting lines. To find linear pairs, look for adjacent angles whose noncommon sides are opposite rays.

  15. ALGEBRA Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle. EXAMPLE 5 Find angle measures in a linear pair

  16. Angle Addition Postulate If P is in the interior of , then the measure of is equal to the sum of the measures of and .

  17. Vocabulary To show that two angles in a diagram are congruent, we put an arc inside each angle.

  18. Assignment • p. 38: 3-27(odds)

More Related