plane geometry

Chapter 5 – Plane Geometry

5-1 Points, Lines, Planes, and Angles5-2 Parallel and Perpendicular Lines5-3 Triangles5-4 Polygons5-5 Coordinate Geometry5-6 Congruence5-7 Transformations5-8 Symmetry5-9 Tessellations

5-1 Points, Lines, Planes & Angles

Vocabulary Point – Names a location Line – Perfectly straight and extends in

both directions forever Plane - Perfectly flat surface that extends

forever in all directions Segment – Part of a line between two

points Ray – Part of a line that starts at a point

and extends forever in one direction

Point

A

Line

A B

Segment

A B

Ray

A

B

Example 1

• Name four points

• Name the line

• Name the plane

• Name four segments

• Name five rays

Q R S

T

m

More Vocabulary Right Angle – Measures exactly 90° Acute Angle – Measures less than 90 ° Obtuse Angle – Measures more than 90 ° Complementary Angle – Angles that

measure 90 ° together Supplementary Angle – Angles that

measure 180 ° together

Right Angle

Acute Angle

Obtuse Angle

Complementary Angle

Supplementary Angle

Example 2

• Name the following:

• Right Angle

• Acute Angle

• Obtuse Angle

• Complementary Angle

• Supplementary Angle

A

B

C

D

E

Q

Even MORE Vocabulary Congruent – Figures that have the same

size AND shape

Vertical Angles Angles A & C are VA Angles B & D are VA

If Angle A is 60° what is the measure of angle B?

A

B

CD

Homework/Classwork

Page 225, #13-34

5-2 Parallel and Perpendicular Lines

Vocabulary Parallel Lines – Two lines in a plane that

never meet, ex. Railroad Tracks Perpendicular Lines – Lines that

intersect to form Right Angles Transversal – A line that intersects two or

more lines at an angle other than a Right Angle

Parallel Lines

A

BC

D

Perpendicular Lines

W

X

Y Z

Transversal

Transversals to parallel lines have interesting properties

The color coded numbers are congruent

1 234

5 678

Properties of Transversals to Parallel Lines

If two parallel lines are intersected by a transversal: The acute angles formed are all congruent The obtuse angles are all congruent And any acute angle is supplementary to any

obtuse angle If the transversal is perpendicular to the

parallel lines, all of the angles formed are congruent 90° angles

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Symbols Parallel

Perpendicular

Congruent

Example 1 In the figure Line X Y

Find each angle measure

X

Y

110

1

2 34

5

6 7

In the figure Line A B

Find each angle measure

A B

30

12

34

567

Homework/Classwork

Page 230, # 6-20

5-3 Triangles Triangle Sum Theorem – The angle measures of

a triangle in a plane add to 180° Because of alternate interior angles, the following is true:

41 mm 53 mm

18021 mmm

Vocabulary Acute Triangle – All angles are less than

90°

Right Triangle – Has one 90° angle

Obtuse Triangle – Has one obtuse angle

Example Find the missing angle

Example Find the missing angle.

Example Find the missing angles

Vocabulary Equilateral Triangle – 3 congruent sides

and angles

Isosceles Triangle – 2 congruent sides and angles

Scalene Triangle – No congruent sides or angles

Equilateral Triangle

Isosceles Triangle

Scalene Triangle

Remember…they are ALL triangles

Example Find the missing angle(s)

Example Find the missing angle(s)

Example Find the missing angle(s)

Example Find the angles. Hint, remember the

triangle sum theorem

Classwork/Homework

Page 237, #10-26

5-4 Polygons Polygons

Have 3 or more sides Named by the number

of sides “Regular Polygon”

means that all the sides are equal length

Polygon # of Sides

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Octagon 8

n-gon n

Finding the sum of angles in a polygon Step 1:

Divide the polygon into triangles with common vertex

Step 2: Multiply the number of triangles by 180

The Short Cut 180°(n – 2) where n

= the number of angles in the figure

In this case n = 6 = 180°(6 – 2) = 180°(4) = 720°

*Notice that n - 2 = 4

**Also notice that the figure can be broken into 4 triangles…coincidence? I don’t think so!

Squares4 congruent sides4 congruent angles

Parallelograms2 pairs of parallel sides

Rectangles4 right angles

Trapezoidsexactly 1 pair of parallell sides

Rhombus4 congruent sides

Quadrilaterals

Example Find the missing angle

This chart may help…

Polygon # of Sides

Total Angle

measure

Triangle 3 180°

Quadrilateral 4 360°

Pentagon 5 540°

Hexagon 6 720°

Heptagon 7 900°

Octagon 8 1080°

n-gon n n°

Classwork/Homework

Page 242, # 13-24