# 1 -3 and 1-4 Measuring Segments and Angles - PowerPoint PPT Presentation

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1 -3 and 1-4 Measuring Segments and Angles. B. A. 4. 10. 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 .

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1 -3 and 1-4 Measuring Segments and Angles

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## 1-3 and 1-4 Measuring Segments and Angles

B

A

4

10

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 |

B

B

D

6

A

A

C

6

D

C

C

B

A

## Postulate 1-6 Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and C, thenAB + BC = AC

• If GJ = 32,

• find x

• find GH

• find HJ

• If AX = 45,

• find y

• find AQ

• find QX

A

B

C

A midpoint of a segment is a point that divides the segment into two congruent segments.

• B is the midpoint of AC

• AB  BC

• 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

D

C

O

B

A

Postulate 1-7 Protractor Postulate

Let OA and OB be opposite rays in a plane. OA, OB and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real number from 0 to 180 in such a way that:

a. OA is paired with 0 and OB is paired with 180

b. If OC is paired with x and OD is paired with y, then mCOD = | x – y |

Acute: 0 < x < 90

Right: x = 90

Straight: x = 180

Obtuse: 90 < x < 180

Angles can be...

• Postulate 1-8 Angle Addition Postulate

• If point B is in the interior of AOC, then mAOB + mBOC = m AOC.

• If AOC is a straight angle, then mAOB + mBOC = 180.

Angles with the same measure are congruent.

If m1 = m2, then 1 2

Congruent

“curtains”