ANGLES Geometry 1.3a. State Standard: LG.1.G.4Geometry Apply, with and without appropriate technology, definitions, theorems, properties, and postulates.

ANGLES

Geometry 1.3a

State Standard:

LG.1.G.4 GeometryApply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics and complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines.

Vocabulary

acute angle - an angle whose measure is between 0 and 90.

adjacent angles - two coplanar angles that share a vertex and a side but do not overlap.

angle - two non-collinear rays having the same vertex

Vocabulary continued…

complementary angles - two angles whose measures add up to 90 degrees.

congruent - having the same measure; having the same size and shape.

obtuse angle - an angle whose measure is between 90 and 180.

Vocabulary continued…

linear pair of angles - two adjacent angles whose non-shared rays form a straight angle.

1 2

right angle – an angle whose measure is exactly 90°.

Vocabulary continued…

supplementary angles - two angles whose measures add up to 180 degrees.

vertex of an angle – the common endpoint of the sides of an angle.

Question: What is the difference in a linear pair and supplementary angles?

Last One…

vertical angles - non-adjacent, non-overlapping congruent angles formed by two intersecting lines (They share a common vertex.)

1 and 3 are vertical angles.

2 and 4 are vertical angles.

12

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Let’s talk about angles…

NOTE: If we name an angle by its vertex alone, there can only be one angle at that vertex…

Parts of an angle:

vertexside

angle measuredin degrees

What do you remember?

Congruent Angles:

Congruent angles do not necessarily have congruent side.

Types of angles:

Which angles are linear pairs?

Naming Angles

Why can’t we call it ⁄ E?

Types of angles:

Angle Addition Postulate

Examples

Examples

Types of Angles

Vertical Angles Theorem

Identify the Second Angle

Supplementary Angles

Complementary Angles

Examples

Examples