1.2 – Segments and Congruence

Distance

Congruent Segments

Positive length between two points

Segments with the same length

CDAB

CDAB A B

C

D

PostulateRules of geometry that are not proved

Ruler Postulate

The distance between 2 points is the absolute value of the difference between them.

1 2 3 4 5 6 7 8

7 – 2 = 5u 2 – 7 = 5u

Segment Addition Postulate

Adding two pieces of a segment total the whole

A B C

AB + BC = AC

1. Measure the length of the segment to the nearest tenth of a centimeter.

AB = ________cm 3.5

1. Measure the length of the segment to the nearest tenth of a centimeter.

CD = ________cm 1.6

1. Measure the length of the segment to the nearest tenth of a centimeter.

EF = ________cm 2.7

2. Find the indicated length.

GJ = _______

16

16u

2. Find the indicated length.

ST = _______

37 – 18 = 19

19u

2. Find the indicated length.

YZ = _______

2x + 3 + 3x – 1 = 27

5x + 2 = 27 -2 -2

5x = 25x = 5

YZ = 3(5) – 1 YZ = 15 – 1 YZ = 14

14u

3. Name the congruent segments using proper notation.

CDAB

CBAD

4. Use the number line to find the indicated measure.

JK = _____ KL = _____

JL = _____ MK = _____

5u 4u

9u 10u

5. Plot the given points in a coordinate plane. Then determine whether the line segments named are congruent.

A(2, 2), B(2, –1), C(0, –2), D(3, –2)

CDAB and

A

BC D

AB = 3u

CD = 3u

CDAB

5. Plot the given points in a coordinate plane. Then determine whether the line segments named are congruent.

E(–3, 2), F(1, 2), G(2, 3), H(2, –2)

GHEF and EF = 4u

GH = 5uE F

G

H

Not congruent

6. In the diagram, points P, Q, R, and S are collinear, PS = 46, PR = 18, and PQ = QR. Find the indicated length.

PQ = QR =

QS =

RS =

46

18

99

28

9u

9u

37u

28u

7. Point J is between H and K.. Use the given information to draw a diagram and write an equation in terms of x. Solve the equation. Then find HJ and JK.

HJ = 2x – 5 JK = 6x HK = 27

H J K2x – 5 6x

27

2x – 5 + 6x = 278x – 5 = 27

+5 +58x = 328 8

x = 4

HJ = 2(4) – 5HJ = 8 – 5HJ = 3u

JK = 6(4)JK = 24u

HJ + JK = HK

7. Point J is between H and K.. Use the given information to draw a diagram and write an equation in terms of x. Solve the equation. Then find HJ and JK.

HJ = 4x + 7 JK = 5x – 8 HK = 53

H J K4x + 7 5x – 8

53

4x + 7 + 5x – 8 = 539x – 1 = 53

+1 +19x = 549 9

x = 6

HJ = 4(6) + 7HJ = 24 + 7HJ = 31u

JK = 5(6) – 8 JK = 30 – 8

HJ + JK = HK

JK = 22u

HW Problem

# 22

Compass, ruler, and protractor, and calculator dueBook Cover and Syllabus Due Monday!!!!!!

VW = 22

Section Page #

Assignment Spiral ?s

1.2 12-13 3-19 odd, 21-26, 28, 29(draw picture for #21-26 and #28-29)

3-5

20

1010

52

1022