Warm-up 1)What 1)What is the notation for angle with vertex at A and whose rays pass through points B and C? 2)What 2)What is the definition of an angle?

Warm-up1) What is the notation for angle with vertex at A

and whose rays pass through points B and C?2) What is the definition of an angle?

Chapter 4 Angles and Measurement

4.1 Angle Measure

Protractor Postulate. For every angle A there corresponds a positive real number less than or equal to 180. This is symbolized 0<m∠A≤180.

Note: m∠A means the measure of an angle where as ∠A is just the angle shape.

Definition:The measure of an angle is the real number that corresponds to a particular angle.Angles are measured in degrees. A circle is broken

into 360 equal divisions called degrees.The instrument used to measure angles is called a

protractor.

Postulate 4.2 Continuity Postulate. If k is a half-plane determined by AC, then for every real number, 0< x≤180, there is exactly one ray, AB, that lies in k such that m ∠BAC = x.Angles are classified according to their angle measure:

Angle name Angle measureAngle name Angle measure

Acute angle 0°< x < 90°

Angle name Angle measure

Acute angle 0°< x < 90°

Right angle x = 90°

Angle name Angle measure

Acute angle 0°< x < 90°

Right angle x = 90°

Obtuse angle 90° < x < 180°

Angle name Angle measure

Acute angle 0°< x < 90°

Right angle x = 90°

Obtuse angle 90° < x < 180°

Straight angle X = 180°

Congruent angles are angles that have the same measure.

Since the measures of the two angles are equal the two angles are congruent.

In symbols: Since m∠BAC= m∠YXZthen∠BAC ≅∠YXZ

YB

C XA Z50° 50°

Cont of 4.1 Angle Measure

Warm-up1) Make a table of the 4 different angles we

learned about. Make sure to include the possible angle measures for each.

Cont of 4.1 Angle Measure

Geometry ToolsStraight Edge – is any tool that can be used to

draw a straight line.Compass – is a tool that has two points that

come in contact with a surface. One point is a stationary point and the other marks the surface. -This tool is used to make arcs or circles.

Protractor – is a tool that is used to measure angle measures.

Ruler – is a tool that is used to measure segment length.

Sketch vs Draw vs Construct.When you sketch a geometric figure you use

just a pencil and no other tools.When you construct a geometric figure you

use only a straight edge and a compass.When you draw a geometric figure you can

use any tools, including tools used for measuring.

Drawing and measuring angles.To measure the degree of an angle:

1) place the hole or vertical slash mark of the protractor at the vertex of the angle.

2) Align one ray with the zero mark of the protractor.

3)The place where the other ray intersects the protractor indicates the measure of the angle.

Drawing and measuring angles.To draw an angle:

1) Draw a ray, this will be one side of the angle.2) Place protractor so that the vertex is

on the hole or vertical slash mark of the protractor.3) Make sure the zero mark is along the

original ray.4) Mark a point at the desired angle measure.5) Draw a ray that goes from the vertex of the original ray through the point.