1.5: MEASURING SEGMENTS AND ANGLES

Prentice Hall Geometry

COORDINATE : The numerical location of a point on a number line.

Length :Length : On a number line length AB = AB = |B - A|

Midpoint :Midpoint : On a number line, midpoint of AB = 1/2 (B+A)

BA C D E

2 4 6 8-2-4-6-8 -1 0

Find the length of each segment.

XY = | –5 – (–1)| = | –4| = 4

ZY = | 2 – (–1)| = |3| = 3

ZW = | 2 – 6| = |–4| = 4

Find which two of the segments XY, ZY, and ZW are congruent.

Because XY = ZW, XY ZW.

GEOMETRY LESSON 1-4GEOMETRY LESSON 1-4

MEASURING SEGMENTS AND ANGLES

THE 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

Use the Segment Addition Postulate to write an equation.

AN + NB = AB Segment Addition Postulate(2x – 6) + (x + 7) = 25 Substitute.

3x + 1 = 25 Simplify the left side. 3x = 24 Subtract 1 from each side. x = 8 Divide each side by 3.

AN = 10 and NB = 15, which checks because the sum of the segment lengths equals 25.

If AB = 25, find the value of x. Then find AN and NB.

AN = 2x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15 Substitute 8 for x.

Use the definition of midpoint to write an equation.

5x + 45 = 8x Add 36 to each side.

RM and MT are each 84, which is half of 168, the length of RT.

M is the midpoint of RT. Find RM, MT, and RT.

RM = 5x + 9 = 5(15) + 9 = 84MT = 8x – 36 = 8(15) – 36 = 84

Substitute 15 for x.

RT = RM + MT = 168

RM = MT Definition of midpoint5x + 9 = 8x – 36 Substitute.

45 = 3x Subtract 5x from each side. 15 = x Divide each side by 3.

HOMEWORK: P. 33 (2-14EVENS, 29-37, 39-43, 45-52 WRITE OUT SENTENCES

QUIZ TOMORROW!!