Points, Lines, and Angles

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Presentation transcript:

Points, Lines, and Angles Chapter 2 Points, Lines, and Angles

Goal Tell type of angle. Label angles. Measure angles.

Review

A? B? C? a ) ray b) line segment c) line

Check a ) ray b) line segment c) line

Review all

angle a figure formed by the intersection of two rays

angle Rays are called sides. Point where sides intersect is called a vertex.

angle examples non-examples

Naming angles Method 1 angle x angle y Method 2 angle ABC angle CBA

Unit of measurement is degrees

List everything you can tell about this angle.

-Angle – 2 rays that intersect -Sides – rays - Point where rays intersect – vertex - Angle ABC or CBA -Measured in degrees - 60 degrees

Types of Angles

Right Angle Right angle an angle whose measure is 90 degrees

right angles orientation – direction still right angle

right angles not right angles

Acute angle acute angle an angle whose measure is less than 90 degrees

acute angles not acute angles

obtuse angle obtuse angle an angle whose measure is greater than 90 degrees but less than 180 degrees

Why are these obtuse angles? examples of obtuse Obtuse angle

Obtuse Angles Not Obtuse

What type of angle? Why? Check again

Why type of angle? A? B? C? D? E? F? acute right angle obtuse

acute right angle obtuse

straight angle straight angle an angle whose measure is 180 degrees

straight angles not straight angles

Page 28 number 1 - 10 measure of angle ARF 180 degrees straight angle measure of angle CRF 120 degrees obtuse 3. measure of angle BRF 155 degrees obtuse

adjacent angles adjacent angle two angles have same vertex share one ray

List adjacent angles Adjacent angles

List adjacent angles Adjacent angles

adjacent angles not adjacent angles

Page 29 1.Angle CDB is adjacent to angle _____ 2. Angle TUV is adjacent to angle ____ 3. Angle SRP is adjacent to angle ____

vertical angles Vertical angles When two lines intersect two pairs of vertical angles are formed

vertical angles Vertical angles are NOT adjacent. Vertical angles have the same measure.

Which angles are vertical?

Which angles are adjacent?

Page 30 Vertical angles 1. angle YPV and angle ____ angle YPV and angle RPS angle QPR and angle _____ angle QPR and angle VPT

complementary angles two angles sum of measures is 90 degrees

a and b angles are complementary even when not connected complementary = sum of angles equals 90 degrees

complementary angles What angles are complementary? Why?

complementary angles Are these angles complementary? Why or Why not?

complementary angles not complementary angles

Supplementary angles two angles sum of measures is 180 degrees

Supplementary angles two angles sum of measures is 180 degrees

Why are figure 1 and figure 2 both examples of supplementary angles? Review 1 obtuse angle 2 acute angle 1 and 2 supplementary

supplementary angles not supplementary angles

Review of Angles

Page 31