Chapter 5 – Plane Geometry 5-1 Points, Lines, Planes, and Angles 5-2 Parallel and Perpendicular Lines 5-3 Triangles 5-4 Polygons 5-5 Coordinate Geometry 5-6 Congruence 5-7 Transformations 5-8 Symmetry 5-9 Tessellations
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