Segments and Angle Bisectors Chapter 1 Section 1.5 Segments and Angle Bisectors

Warm-Up Name an acute angle. EBF or FBD 2. Name an obtuse angle. ABF 3. Use the angle addition postulate to represent: a. mABF mABE + mEBF = mABF b. mEBD mEBF + mFBD = mEBD A B D

Midpoint The midpoint of a segment is the point that divides the segment into two congruent segments Bisect: Two cut a figure in half A B C Midpoint Since B is the midpoint of , then

Segment Bisector A segment, ray, line or plane that intersects a segment at its midpoint Midpoint Segment Bisector • C P Q R • D Since is the Segment Bisector of , then

Use a ruler to measure the segment, and redraw the line segment Use a ruler to measure the segment, and redraw the line segment. Then construct a segment bisector.

Midpoint formula Used to find the midpoint of a segment with known endpoints If A(x1, y1) and B(x2, y2) are the endpoints of segment AB, then the midpoint of segment AB has coordinates

Find the coordinates of the midpoint of a segment with the given endpoints A(-3, 5) and B(5, -1) Use the formula C(-4, -3) and D(6, 3) Use the formula

Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M Use the formula Remember the other endpoint is (x2, y2) 1. Find x2 2. Find y2 The other endpoint is (2, -1)

Find the coordinates of the other endpoint of the segment with the given endpoint and midpoint M Use the formula Remember the other endpoint is (x2, y2) 1. Find x2 2. Find y2 The other endpoint is (2, -13)

Angle Bisector A ray that divides an angle into two congruent adjacent angles • A B C • P If is the angle bisector of BAC, then BAP  PAC

Use a protractor to measure and redraw the angle Use a protractor to measure and redraw the angle. Then use a compass to find the angle bisector.

is the angle bisector of RPS is the angle bisector of RPS. Find the two angle measures not given in the diagram. P R • T • •S 1 37° P • R T • S • 2 44° mRPT = mTPS = 37 ° mRPS = mRPT + mTPS mRPS = 37° + 37 ° mRPS = 74° mRPT = mTPS = 44 ° mRPS = mRPT + mTPS mRPS = 44° + 44 ° mRPS = 88 °

is the angle bisector of ABC. Find the value of x. 3. (5x – 7)° (3x + 13)° Since ABC is bisected thus ABT  TBC Which means: mABT = mTBC 3x + 13 = 5x – 7 -2x + 13 = -7 -2x = -20 x = 10