1-4 Measuring Segments and Angles. AB 5 in Postulate 1-5 Ruler Postulate The point of a line can be put into a one- to-one correspondence with the real.

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Presentation transcript:

1-4 Measuring Segments and Angles

AB 5 in

Postulate 1-5 Ruler Postulate The point of a line can be put into a one- to-one correspondence with the real number so that the distance between any two points is the absolute value of the difference of the corresponding numbers. AB = | a – b | BA 410

Examples— A BC DE CD= BC= EB= DE=

Two segments with the same length are congruent. If AB = CD, then AB ≅ CD ≅ means congruent BA 6 BA DC 6 DC

Postulate 1-6 Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC A B C

Write the Segment Addition Postulate for the points described. Draw a picture to help. S is between D and P C is between Q and R T is between M and N

For each problem, draw a picture representing the three points and the information given. Solve for indicated. If AC = 24 in. and CE = 13 in., AE = _____. If CE = 7in. and AE = 23 in., AC = _____.

Find QR in the following problems. R is between Q and S. If RS = 44.6 and SQ = 68.4, find QR. If RS = 33.5 and RQ = 80, find SQ.

If GJ = 32, find x find GH find HJ If AX = 45, find y find AQ find QX

For each problem, draw a picture representing the three points and the information given. Solve for indicated. Given : AC = 39 m A B C 2x-8 x+17 x = ________ AB = _______ BC = _______

If U is between T and B, find the value of x and the lengths of the segments. TU = 2x, UB = 3x + 1, TB = 21 x = ______ TU = _______ UB = _______ TU = 4x-1, UB = 2x -1, TB = 5x x = ______ TU = _______ UB = _______

A midpoint of a segment is a point that divides the segment into two congruent segments. ABC M is the midpoint of RT find x find RM find RT

An angle  is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle). Angles are measured in degrees. Sides are GC and GA; G is the vertex. Name this angle:  G  3  CGA  AGC

A B D C O

Angles can be... Acute: 0 < x < 90 x° Right: x = 90 x° Obtuse: 90 < x < 180 x° Straight: x = 180

17 Adjacent Angles Two angles are called adjacent angles if they share a vertex and a common side (but neither is inside the opening of the other). Angles 1 and 2 are adjacent: 1 2

Postulate 1-8 Angle Addition Postulate If point B is in the interior of  AOC, then m  AOB + m  BOC = m  AOC.

19 Example A M T H

Angles with the same measure are congruent. If m  1 = m  2, then  1   2 Congruent “ curtains ”

Homework— Page (1, 3, 8-16, 27, 28, 59, 60, 61, , 75-78)