Advanced Geometry Inductive Reasoning Lesson 2

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# Advanced Geometry Inductive Reasoning Lesson 2 - PowerPoint PPT Presentation

Angles. Advanced Geometry Inductive Reasoning Lesson 2. Rays. Drawn as: a line with one endpoint and one arrowhead. N. D. Named by: 2 points and a ray symbol.  the endpoint must be named first.  the arrow always points to the right.

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Presentation Transcript

Angles

Inductive Reasoning

Lesson 2

Rays

Drawn as: a line with one endpoint and one

N

D

Named by: 2 points and a ray symbol

•  the endpoint must be named first

 the arrow always points to the right

Opposite rays are two collinear rays that point in opposite directions.

Angle

Parts of an Angle

vertex – the common endpoint

B

sides – the rays

Regions

interior

exterior

on the angle

Naming an Angle

Use an angle symbol and…

- the number inside the angle.

• three points with the vertex
• in the middle.

- the vertex point.

*You can only use this method if there is ONE angle at the vertex.

Examples:

Name the sides of

Write another name for

Name all angles that have B as

a vertex.

Angle Classifications
• Right angle– measures exactly 90°
• Acute angle – measure is less than 90°
• Obtuse angle– measure is greater than 90° and less than 180°
• Straight angle – an angle with a
• degree measure of exactly 180°
• (a.k.a. straight line)

bisects

Angle Relationships

Adjacent angles are beside each other.

They share a vertex and side.

They do not overlap.

Vertical Angles

They share a vertex only.

Vertical angles are congruent.

Linear Pair

Angles of a linear pair ARE adjacent.

They share a vertex

and a side.

Remember: If two rays are opposite rays, they create a straight line.

Example: Name an angle pair that satisfies each condition.

two angles that form a linear pair

two acute vertical angles

Complementary Angles

two angles

sum of 90

Supplementary Angles

two angles

sum of 180

LINEAR PAIRS ARE

ALWAYS

SUPPLEMENTARY.

Example:

If BCE and ECD are supplementary, find ECF and FCD.

Example:

Find the measures of two supplementary angles if the difference in the measures of the two angles is 32.

The complement of an angle is 3.5 times smaller than the supplement of the angle. Find the measure of the angle.