Warm-up. Fill in the blank with always , sometimes , or never . Explain your answer. A bisector of a segment is ______ a line. A ray ______ has a midpoint. 3. Congruent segments ______ have equal lengths. 4. If B is between A and C , then AB ________ equals BC. R. 1. S. T.
Lesson 1-4 Angles
angle () – a figure formed by two rays that have the same endpoint. The two rays are called sides of the angle.
Their common endpoint is called the vertex.
obtuse angle– an angle with measure between 90 and 180.
right angle– an angle with measure 90.
straight angle– an angle with measure 180.
On AB in a given plane, choose any point O between A and B.
Consider OA and OB and all the rays that can be drawn from
O on one side of AB. These rays can be paired with the real numbers from 0 to 180 in such a way that:
a. OA is paired with 0, and OB with 180.
b. If OP is paired with x, and OQ with y, then POQ = |x – y|.
Use a protractor to measure each angle to the nearest degree. Then,write three names for each angle.
If AOC is a straight angle and B is any point
not on AC,then
Postulate 4Angle Addition Postulate
If point B lies in the interior of AOC,then
mAOB + mBOC = mAOC .
mAOB + mBOC = 180 .
CLE 28-33 all
WE 1-22 all, 26-28 all
Lesson 1-4 Angles (continued)
congruent angles– angles that have equal measures.
If mA = mB, then A B.
adjacent angles (adj. s)– two angles in a plane that have a common vertex and a common side but no common interior points.
1 and 2 are adjacent angles.
3 and 4 are NOT adjacent angles.
If NO bisects MNP, then ___________
bisector of an angle– the ray that divides the angle into two congruent adjacent angles.
Ex. 1) Find each angle measure, given the diagram and information below.
Given: m1 = 5x,
m2 = (x + 40), and
m3 = (x2 – 20)
Ex. 2) Given that AM bisects LAR and AS bisects MAR, find mLAR using the given information.
Given:mRAM = (5x – 7), and
mMAS = (x + 3)
page 22 29-36 all
Read pages 22-23 and complete the outline of Lesson 1-5, including allvocabulary, postulates and theorems
(but NOT the warm-up, examples, or cool-down.