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**Chapter 1 Basics of Geometry**

By: Carly Overleese, Karmen Spiker and Lindsey Lewis

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**Identify the pattern in the picture. What is the next figure?**

1.1 Identify the pattern in the picture. What is the next figure?

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You Try It Now… What is the next three numbers. 15,30,45,60... What is the Pattern? 225,45,11.25,3.75 225,45,11.25,3.75 75,90,105

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**Points, Lines, and Planes**

1.2 Points, Lines, and Planes

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1.2 Line- Plane

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1.2 Line Segment Ray Initial Point Opposite rays

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**Now You Try Draw four noncollinear points. Label A,B,C,D.**

Draw a Segment from AB. Draw a line through BC. Through CD draw a ray. Draw a segment through AD. B C A D

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1.2 Collinear Points- Coplanar Points-

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**Segments and Their Measures**

1.3 Segments and Their Measures

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**1.3 Postulate 1- The Ruler Postulate**

The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The Distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the length of AB. A B

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**1.3 Postulate 2: Segment Addition Postulate**

If B is between A and C, then AB+BC=AC. If AB+BC=AC, then B is between A and C. A C B

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Distance Formula If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is AB= (x2-x1) 2 + (y2-y1)2

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**Using the Distance Formula**

Use the Distance Formula to find the lengths between the two points. A(-1,1) B(-4,3) Try and then we will check it..

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**ANSWER DID YOU GET IT CORRECT? AB= (x2-x1) 2 + (y2-y1)2**

((-4)- (-1))2 +(3-1) 2 (-3)2 +22 9+4 13 DID YOU GET IT CORRECT?

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**Now your turn to try it… AE=20 BD=6 AB=BC=CD**

In the picture of collinear points, AE=20 BD=6 AB=BC=CD D Find Each Length… BC AB AC AD C 3 B A 3 6 9

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**Angles and Their Measures**

1.4 Angles and Their Measures

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Angle

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**What are the two names of the angle?**

Naming Angles What are the two names of the angle? C A L ABC and L CBA B

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**1.4 Postulate 3: Protractor Postulate**

Consider a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180. The measure of L AOB is equal to the absolute value of the difference between the real numbers for OA and OB. A B O

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**1.4 Postulate 4: Angle Addition Postulate**

If P is in the interior of L RST, then mLRSP+mLPST=mLRST R mLRST mLRSP S P mLPST T

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**An angle with a measure between 0 degrees and 90 degrees**

Acute Angle An angle with a measure between 0 degrees and 90 degrees

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**An angle with a measure of 90 degrees.**

Right Angle An angle with a measure of 90 degrees.

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**An angle with a measure between 90 degrees and 180 degrees.**

Obtuse Angle An angle with a measure between 90 degrees and 180 degrees.

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**An angle with a measure of 180 degrees.**

Straight Angle An angle with a measure of 180 degrees.

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Adjacent Angles Two angles with a common vertex and side, but no common interior points.

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**Now your Turn Using the Angle Addition Postulate. What is mLDBC?**

Answer:30° A 60° D B C

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**Segment and Angle Bisectors**

1.5 Segment and Angle Bisectors

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**(x1,y1) (x2,y2) Midpoint Formula**

If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the midpoint of AB has coordinates. (x1,y1) (x2,y2)

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**Your turn Applying Midpoint Formula**

Find the midpoint of AB. A(-2,3) and B(5,-2) ANSWER 3, 1 2 2

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**Angle Pair Relationships**

1.6 Angle Pair Relationships

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**Vertical Angles/ Linear Pair**

Consists of two angles whose sides form two pairs of opposite rays. Consists of two adjacent angles whose non-common sides are opposite rays. 5 6 L1 and L3 are vertical angles. L2 and L4 are vertical angles. L5 and L6 are linear pairs

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**Finding the Angle Measure…**

Find the Measurement of L1. Answer: 150° 30° 1 Answer: 45° 45° 1

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**That concludes Chapter 1. Basics of Geometry.**

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