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GEOMETRIC STRUCTUREChapter 1

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POINTS, LINES, & PLANES

Lesson 1-1

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VOCABULARY

Undefined term Point Line Collinear Plane Coplanar Space Locus

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EXAMPLE 1

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EXAMPLE 2

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EXAMPLE 3A

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EXAMPLE 3B

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EXAMPLE 4

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LINEAR MEASURE & PRECISIONLesson 1-2

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VOCABULARY

line segment precision congruent construction

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EXAMPLE 1

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EXAMPLE 2

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EXAMPLE 3

Find the precision for each measurement. Explain it’s meaning.

a. 5 millimeters

b. 8 ½ inches

c. 10 ¼ inches

d. 12.2 centimeters

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EXAMPLE 4A

Find AC

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EXAMPLE 4B

Find DE

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EXAMPLE 4C

Find y and QP if P is between Q and R. QP = 2y, QR = 3y + 1, and PR = 21.

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EXAMPLE 4D

Find x and BC if B is between A and C. AC = 4x – 12, AB = x, and BC = 2x + 3

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DISTANCE & MIDPOINTLesson 1-3

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VOCABULARY

midpoint segment bisector

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EXAMPLE 1

Use the number line to find CD.

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EXAMPLE 2 – DISTANCE FORMULA

Find the distance between R (5, 1) and S (-3, -3).

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EXAMPLE 2 – PYTHAGOREAN THEOREM

Find the distance between R (5, 1) and S (-3, -3).

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EXAMPLE 3

Find the midpoint of PQ.

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EXAMPLE 4

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

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EXAMPLE 5

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

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EXAMPLE 6

Find the measure of BC if B is the midpoint of AC.

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ANGLE MEASURELesson 1-4

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VOCABULARY

degree ray opposite rays angle sides vertex

interior exterior right angle acute angle obtuse angle angle bisector

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EXAMPLE 1

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EXAMPLE 2

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EXAMPLE 3

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ANGLE RELATIONSHIPSLesson 1-5

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VOCABULARY

adjacent angle vertical angles linear pair complementary

angles supplementary

angles perpendicular

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EXAMPLE 1

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EXAMPLE 2

Find the measures of two complementary angles if the difference in the measures of the two angles is 12.

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EXAMPLE 3

Find x and y so that BE and AD are perpendicular.

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EXAMPLE 4