Chapter 1 Basics of Geometry By: Carly Overleese, Karmen Spiker and Lindsey Lewis

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

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 5 4 3 2 75,90,105

Points, Lines, and Planes 1.2 Points, Lines, and Planes

1.2 Line- Plane

1.2 Line Segment Ray Initial Point Opposite rays

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

1.2 Collinear Points- Coplanar Points-

Segments and Their Measures 1.3 Segments and Their Measures

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

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

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

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..

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?

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

Angles and Their Measures 1.4 Angles and Their Measures

Angle

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

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

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

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

An angle with a measure of 90 degrees. Right Angle An angle with a measure of 90 degrees.

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

An angle with a measure of 180 degrees. Straight Angle An angle with a measure of 180 degrees.

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

Now your Turn Using the Angle Addition Postulate. What is mLDBC? Answer:30° A 60° D B C

Segment and Angle Bisectors 1.5 Segment and Angle Bisectors

(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)

Your turn Applying Midpoint Formula Find the midpoint of AB. A(-2,3) and B(5,-2) ANSWER 3, 1 2 2

Angle Pair Relationships 1.6 Angle Pair Relationships

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

Finding the Angle Measure… Find the Measurement of L1. Answer: 150° 30° 1 Answer: 45° 45° 1

That concludes Chapter 1. Basics of Geometry.