**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**

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