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Geometry: Angle Relationships in Parallel Lines & Triangles

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Yannerys Mullins

on 6 November 2014

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Transcript of Geometry: Angle Relationships in Parallel Lines & Triangles

Content Goals for Geometry
Shapes and Properties: study of shapes and
their properties in both 2 and 3 dimensions and their relationships
.
Transformation: a study of translations (slides), reflections (flips), rotations (turns), symmetry, and similarity.

Location: coordinate geometry or how to locate objects in the plane or in space.

Geometric Thinking

By: Yannerys Mullins
Angles
Angles are classified by their measures.

A
is read "angle A"

m
A
is read "the measure of angle A"

Classifying Angles
An
acute angle
is an angle whose measure is less than 90 degrees.


A
right angle
is an angle whose measure is exactly 90 degrees.

An
obtuse angle
is an angle whose measure is between 90 degrees and 180 degrees.

A
straight angle
is an angle whose measure is exactly 180 degrees.

Two angles are
complementary
if the sum of their measures is 90 degrees.

Two angles are
supplementary
if the sum of their measures is 180 degrees.

Supplementary and Complementary Angles
Example:
28+62=90; complementary
71+109 = 180; supplementary
LINES IN A PLANE
Special Pairs of Angles
Example: Identifying Adjacent Angles
Name all pairs of adjacent,
supplementary angles.
1
2
4
3
angles 1 and 2, angles 2 and 3,
angles 3 and 4, angles 1 and 4

Adjacent Angles
Vertical Angles
When two lines meet at a point the angles that are opposite each other are called
vertical angles
.

Vertical angles are
congruent angles
, meaning they have the same measure.
Example:
1
2
3
4
If m4= 105 , Then m2=
Parallel Lines
A plane is like a flat surface that extends without an
end. In diagrams, planes appear as shown at the
right.Two lines that meet at a point are called
intersecting lines.
Two lines in the same plane that do not intersect are called
parallel lines
.
The symbol
ll
is used to indicate parallel lines.
Perpendicular
Lines
Perpendicular lines intersect to form four right angles.
They are indicated by the symbol

Corresponding Angles
Parallel lines in a plane (m
ll
n)
Perpendicular lines in a plane (a b)
Angles that occupy corresponding positions when a line intersects two other lines are called corresponding angles.
When a line intersects two parallel lines, corresponding angles are congruent.
Example
1. Name a street parallel
to Elm Street.
2. Name two streets that intersect 1st Ave.
3. Find the measures of angles 1, 2, 3, 4, 5, and 6.
Solutions:
1. Main St.
2. Elm St. and Main St.
3. Angle 1 = 123, Angle 2 = 99, Angle 3= 123, Angle 4= 123, Angle 5= 99, Angle 6 = 99
Two angles on a flat surface that share a common side and a vertex and do not overlap are called adjacent angles.
When two lines meet at a point, adjacent angles are supplementary.
Solution: Angle 4 & 2 are
vertical angles therefore
congruent angles which
have the same
measurements
Triangles
- Triangles consist of 3 angles. Each angle must be 90 degrees or less.
- In an acute triangle, every angle is less than 90 degrees.
- In an obtuse triangle, one of the angles is greater than 90 degrees.
-In a right triangle, one angle is 90 degrees.
There are three types of triangles.
Equilateral: All sides are the same length
Isosceles: Two or more sides can be the same length (therefore, an equilateral triangle also counts as an isosceles triangle)
Scalene: All three sides are different lengths
Triangles
http://studyjams.scholastic.com/studyjams/jams/math/geometry/classify-triangles.htm
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