1. Date: Topic: Segment and Angles (11.3) Warm-up: Use the figure to name the indicated angle in two different ways. A T H M 1 2 Why can’t you use to name any angles in the diagram? There are multiple angles created with vertex A. It would be unclear which angle is being referred to. Naming an angle using only the vertex letter can only be used if there is only one angle in the visual representation.

2. The midpoint of a segment is the point that divides it into two segments of equal length. A bisector of a segment is any line, segment, ray, or plane that intersects the segment at its midpoint. AB l Z M is the midpoint of M AMMB= andbisectLine lPlane Z The Midpoint Theorem: If point M is the midpoint of, then

3. Find the midpoint of the midpoint is half the length: -3-201234567 PUYRQSTVWXZ the midpoint is 3 units from either endpoint 33 T is the midpoint of PRS 3n - 5n + 7 In the figure below, point R is the midpoint of. Find the length of. -n +5 2 2 There is a Midpoint formula T is the midpoint.

4. The Angle Bisector Theorem: If is the bisector of, then X C A B If what is the measure of ? Since is the angle bisector then is half of : 54˚

5. Complete the two-column proof: 1. Given 3. Definition straight angle 4. Transitive Property Statements Reasons Given: Prove: 1. 3. 4. 2. Definition straight angle2. 3 4 1 2 B E C D A 5. Reflexive Property 6. Transitive Property of Addition 5. 6.

6. Find the measure of angle : vertical angles are equal 5n - 28 = 2n + 20 -2n +28 3n = 48 3 n = 16˚ X (2n+20)˚(5n-28)˚ E A C R substitute to find angle Vertical Angles Theorem: If two angles are vertical angles, then they are equal in measure. and are vertical angles and equal 3 4 1 2