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 .

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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

1-3 and 1-4 Measuring Segments and Angles


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 |


Two segments with the same length are congruent if ab cd then ab cd means congruent

B

B

D

6

A

A

C

6

D

C

Two segments with the same length are congruent.If AB = CD, then AB ≅ CD≅ means congruent


1 3 and 1 4 measuring segments and angles

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


1 3 and 1 4 measuring segments and angles

  • If GJ = 32,

  • find x

  • find GH

  • find HJ

  • If AX = 45,

  • find y

  • find AQ

  • find QX


1 3 and 1 4 measuring segments and angles

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


1 3 and 1 4 measuring segments and angles

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


1 3 and 1 4 measuring segments and angles

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 |


1 3 and 1 4 measuring segments and angles

Acute: 0 < x < 90

Right: x = 90

Straight: x = 180

Obtuse: 90 < x < 180

Angles can be...


1 3 and 1 4 measuring segments and angles

  • 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.


1 3 and 1 4 measuring segments and angles

Angles with the same measure are congruent.

If m1 = m2, then 1 2

Congruent

“curtains”


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