Chapter 1 Section 6 Angles Geometry Chapter 1 Section 6 Angles

Rays A Ray has one endpoint and goes forever in one direction A Ray is named with the endpoint and one point on the ray

The Ray A B Is called Ray BA never Ray AB

Name The Ray R G

Angle 2 rays with a common endpoint The common endpoint is called the Vertex The rays are called Sides Side Vertex Side

Name an angle G T B L G L TGB L 1 With the angle Sign L and: The vertex A Point on one side, the vertex and a point on the other A number designator L G L TGB L 1

Interior and exterior of an angle

3 Letter Angle Name A 3 letter angle name must be used if more than one angle shares a vertex T R F S If you named an angle L R Would you refer to L TRF , L TRS or L SRF?

To Read an angle name Pick the first letter is on a side, the middle letter is the vertex, and the third letter is on the other side L BTG B G T V C Z E

To Read an angle name L BTZ L BTG L CVE L EVT L ZTV L GTV L BTV L ZTG

Angle Measurement Angles are measured in degrees All Angles have measurements between 0 and 1800 The restrictions on an angle are 00 ≤ any angle ≤ 1800

Special angles An angle of measure 00 is a ray An Angle of measure 1800 is called a Straight Angle A Straight Angle is formed by Opposite Rays An angle with a measure of 900 is called a Right Angle

Angle Congruence If 2 angles have the same measure then they are congruent If L Q @ L R then m L Q = m L R Q R

Angle Addition Postulate If R is on the interior of angle PQS Then m L PQR + m L RQS = m L PQS P Q R S

Angle Addition Postulate L GFE = 3x + 7 L DFG = 4x + 20 L EFD = 5x + 3 find x find L DFG G F E D

Classifying Angles 00 < angle < 900 Acute Degree Measure Classification 00 < angle < 900 Acute 900 < angle < 1800 Obtuse angle = 900 Right angle = 1800 Straight

Restrictions on an Angle If L NHM is Obtuse then 900 < L NHM < 1800 If L KJW is Acute then 00 < L NHM < 900

Restrictions on an Angle If L NHM is Obtuse and L NHM = 2x+4 then find the restrictions on x 900 < L NHM < 1800 90 < 2x+4 < 180 86 < 2x < 176 43 < x < 88

Restrictions on an Angle If L DRW is Obtuse and L DRW = 3x + 9 find the restrictions on x ___0 < L DRW < ___0

Angle Bisector If L GFE @ L EFD then FE is an angle bisector of L GFD An Angle Bisector is a Ray that divides an angle into 2 @ angles G If L GFE @ L EFD then FE is an angle bisector of L GFD F E D

If FE is an angle bisector of L GFD and L GFD = 5x -3 L GFD = 2x +12 Find L EFD G F E D

Do Now Page 49 - 51 Problems 10 – 12 17 – 28 33 – 39 42 - 49