G EOMETRIC S TRUCTURE Chapter 1 1

P OINTS, L INES, & P LANES Lesson 1-1 2

V OCABULARY Undefined term Point Line Collinear Plane Coplanar Space Locus 3

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E XAMPLE 1 5

E XAMPLE 2 6

E XAMPLE 3 A 7

E XAMPLE 3 B 8

E XAMPLE 4 9

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L INEAR M EASURE & P RECISION Lesson

V OCABULARY line segment precision congruent construction 12

E XAMPLE 1 13

E XAMPLE 2 14

E XAMPLE 3 Find the precision for each measurement. Explain it’s meaning.  5 millimeters  8 ½ inches  10 ¼ inches  12.2 centimeters 15

E XAMPLE 4 A Find AC 16

E XAMPLE 4 B Find DE 17

E XAMPLE 4 C Find y and QP if P is between Q and R. QP = 2y, QR = 3y + 1, and PR =

E XAMPLE 4 D Find x and BC if B is between A and C. AC = 4x – 12, AB = x, and BC = 2x

D ISTANCE & M IDPOINT Lesson

V OCABULARY midpoint segment bisector 21

E XAMPLE 1 Use the number line to find CD. 22

E XAMPLE 2 – D ISTANCE F ORMULA Find the distance between R (5, 1) and S (-3, -3). 23

E XAMPLE 2 – P YTHAGOREAN T HEOREM Find the distance between R (5, 1) and S (-3, -3). 24

E XAMPLE 3 Find the midpoint of PQ. 25

E XAMPLE 4 Find the coordinates of M, the midpoint of JK, for J (,- 1, 2) and K (6, 1). 26

E XAMPLE 5 Find the coordinates of X if Y (-1, 6) is the midpoint of XZ and Z has coordinates (2, 8). 27

E XAMPLE 6 Find the measure of BC if B is the midpoint of AC. 28

A NGLE M EASURE Lesson

V OCABULARY degree ray opposite rays angle sides vertex interior exterior right angle acute angle obtuse angle angle bisector 30

E XAMPLE 1 31

E XAMPLE 2 32

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E XAMPLE 3 34

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A NGLE RELATIONSHIPS Lesson

V OCABULARY adjacent angle vertical angles linear pair complementary angles supplementary angles perpendicular 39

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E XAMPLE 1 41

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E XAMPLE 2 Find the measures of two complementary angles if the difference in the measures of the two angles is

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E XAMPLE 3 Find x and y so that BE and AD are perpendicular. 45

E XAMPLE 4 46