1 -3 and 1-4 Measuring Segments and Angles

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

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

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...