Geometry



Geometry Name_____________________________

CH 1 Study Guide Date__________________

                                                        VOCABULARY

|point                                        line                                     plane                  angle |

|collinear points                       line segment                      ray                      sides |

|opposite rays                           intersect                            linear pair          vertex |

|midpoint formula                   angle bisector                   acute angle         bisect |

|segment addition postulate   collinear plane                  midpoint             vertical angle |

|supplementary angles            distance formula              obtuse angle       congruent angle |

|complementary angles           congruent segments         right angle          straight angle |

|angle addition postulate         adjacent angles                segment bisector |

1.2 Points, Lines, Planes

Point – represents a location, no size, no thickness         .A

Line – infinite set of points, no thickness, extends in both directions forever (straight line)

Name - line m, [pic]

Plane – Flat surface that extends forever, made up of infinite points and lines

             Must be 3 points not in a line

             Plane M,   Plane ABC

                                                                       

Collinear Points – all points that lie on the same line

Collinear Plane – all points that lie on the same plane

Line Segment – Consists of 2 endpoints and all the points between them

                               [pic]

Ray – The ray AB consists of the initial point A and all the points that lie on the same     side of A as point B

                                                                                                      

Opposite Rays –– 2 rays that share exactly 1 point. If C is between A and B, then [pic] are opposite rays.

                                     

Intersect – 2 or more geometric figures intersect if they have 1 or more points in common.

Intersecting Planes Line Interesting Plane

2 planes intersect in a line.

                      

1.3 Segments and Their Measures

Distance/Length – same meaning

[pic] = line segment AB

AB = refers to the length of segment AB

[pic] = line AB

[pic] = ray AB

Between refers to collinear points. When 3 points lie on a line, you can say that one of them is between the other two.

Distance Formula

AB =   [pic]

Find the length of the segments. 

AB = [pic]

[pic]

[pic]

[pic]

                                                                                             

Congruent Segments – segments that have the same length

                      

                [pic]  [pic] (is congruent to)

                   

Segment Addition Postulate – If B is between A and C then AB + BC =AC

                               

1.4 Angles and Their Measures

Angle – 2 different rays that have the same initial point

Sides – the rays that make up the angle. [pic]

Vertex – the initial point of the angle  

                                                                

Name –  [pic]

Measure = [pic]

Congruent angles – angles that have the same measures

A point is in the interior of an angle if it is between points that lie on each side of the angle.

A point is in the exterior of an angle if it is not on the angle or in its interior.

Angle Addition Postulate – If P is in the interior of    [pic]

                                                                                   

Acute angle – an angle with measure between 0 and 90

                                  

                

Right angle – an angle with measure equal to 90                                     

                                

Obtuse angle – an angle with measure between 90 and 180

                              

                                  

Straight angle – an angle with measure equal to 180

                        

[pic]

Adjacent angles – 2 angles that share a common vertex and side, but have no common interior points

  

                                      [pic]are adjacent angles

1.5 Segment and Angle Bisectors

Midpoint – the point that divides segment into two congruent segments.

                                              

Bisect – to divide into 2 congruent parts

Segment bisector – a segment, ray, line, or plane that intersects a segment at its midpoint

                                           

Midpoint Formula – If A(x ,y  ) and B(x ,y ) endpoints of a segment then the midpoint of AB is 

[pic]

Find the coordinates of the midpoint of AB with A(-2,3) and B(5,-2)

                                 

Angle Bisector – a ray that divides an angle into 2 adjacent angles that are congruent.

                                               

       

                        

1.6 Angle Pair Relationships

Vertical Angles – 2 angles whose sides form 2 pairs of opposite rays

                                        [pic]    

Linear Pair – 2 adjacent angles whose non common sides are opposite rays

                      [pic]                         

Complementary Angles – 2 angles whose measures have the sum 90

  Complementary adjacent                       Complementary nonadjacent

                                                                              

                                        

Supplementary Angles – 2 angles whose measures have the sum 180

  Supplementary adjacent   Supplementary nonadjacent

1.7 Introduction to Perimeter, Circumference, and Area

Formulas

Square

            P = 4s

[pic] 

   

Rectangle

            Length l and width w

            P = 2l + 2w

Triangle

            Side lengths a, b, and c, base b, and height h

            P = a+b+c

[pic]

Circle

            Radius r

           [pic] 

           [pic]

           

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A

B

C

D

m

A

B

C

B

A

A

B

C

20

120

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