Geometry Lesson 1 4 Angle Measure Objective Measure

Geometry Lesson 1 – 4 Angle Measure Objective: Measure and classify angles. Identify and use congruent angles and the bisector of an angle.

Ray – has a definite starting point and extends without end in one direction. The starting point of a ray is called the endpoint. A ray is named using the endpoint first, then another point on the ray. *Naming a ray: arrow always points right!

Ray cont… Look at the pairs of rays

Opposite Rays Opposite rays are rays that have collinear points and share only one point. Opposite rays:

Angle is formed by noncollinear rays.

Naming Angles More than one way to name: l Name by letters (follow the sides) l Vertex l Name is always middle letter by vertex l *Warning* l Name Only use if there is one angle by number (only if given)

Name the angle in all ways

Example Name the angle in four ways. Then identify its vertex and its sides. Vertex: B Sides:

Name the whole angle in as many ways as possible Cannot use vertex to name because there are 3 angles with vertex P not one. Cannot use number to name because there is not a number that represents the whole angle.

Angle divides a plane

Example Nam all angles that have B as a vertex. Name the sides of Write another name for

Name all angles having W as their vertex.

Degrees Angles are measured in units called degrees. l 360 degrees in a circle. l 1 degree is 1/360 of a circle. Use protractors to measure degrees.

Reading math Read the following: l read as “angle DEF” l read as “the measure of angle DEF”

Types of angles Right l An angle with a degree of 90 Acute l An angle whose measure is less than 90 l 0 < x < 90 Obtuse l An angle whose measure is greater than 90 l 90 < x < 180

Classifying angles Classify each angle as right, acute, or obtuse. Obtuse Right Acute

Use a protractor to measure Find the measure of Start at the one side and go ‘up’ to the other side starting at 0. Or think of it as: The angle is acute so the angle is 45 degrees. (not 135)

115 85 65

Using a Protractor To measure an angle Place the vertex of the angle on the ‘dot’ of the protractor l Line up on side of the angle with the line on the protractor l Read the protractor where the other side crosses. l

Find the measure of the angle. 40

Find the measure 45 100 150

Classify each angle and measure to the nearest degree. Right, 90 degrees Obtuse, 105 degrees Acute, 20 degrees

Classify each angle and measure to the nearest degree. Acute, 20 degrees Obtuse, 125 degrees Acute, 25 degrees

Congruent Angles **Notice that = is used when talking about the measure and congruent is used when talking about the angles.

Angle bisector A ray that divides an angle into 2 congruent parts. Ray YW is an angle bisector.

Example KJ and KM are opposite rays, and KN bisects 8 x – 13 = 6 x + 11 since ray KN bisects the angle. 2 x – 13 = 11 2 x = 24 x = 12

Example Suppose 2(5 y + 2) = 9 y + 15 10 y + 4 = 9 y + 15 y + 4 = 15 y = 11 Smaller angle is half bigger angle Or 2 times smaller = bigger