Obj. 5 Measuring Angles Objectives: Correctly name an angle Identify acute, right, obtuse, and straight angles Set up and solve linear equations using the Angle Addition Postulate and angle bisector properties Use a protractor to measure and draw angles Construct a congruent angle and angle bisector

A figure formed by two rays or sides with a common endpoint. angle vertex A figure formed by two rays or sides with a common endpoint. Example: The common endpoint of two rays or sides (plural vertices). Example: A is the vertex of the above angle ● A C R

Notation: An angle is named one of three different ways: 1. By the vertex and a point on each ray (vertex must be in the middle) : TEA or AET By its vertex (if only one angle): E 3. By a number: 1 ● E T A 1

Which name is not correct for the angle below? Example Which name is not correct for the angle below? TRS SRT RST 2 R S R ● ● 2 ● T

Measuring Angles Draw a ray on your paper about 3“ long. Draw another ray about 3“ long connected to it, creating an acute angle. Label the vertex A. Line the center mark of your protractor at the vertex and the 0º/180º marking along one side (different protractors use different methods of alignment). Count up from 0º to where the other side crosses the protractor’s edge. That number is the measure of angle A.

obtuse angle right angle acute angle straight angle Angle whose measure is greater than 90˚ and less than 180˚ Angle whose measure is exactly 90˚ Angle whose measure is less than 90˚ Angle whose measure is exactly 180˚ (a straight line) According to these definitions, did you draw an acute angle?

Constructing a Congruent Angle Draw an acute angle. Label the vertex I. Draw a ray at least 3“ long and label the endpoint H. Place the point of your compass at point I and draw an arc that intersects both sides of I. Label the intersection points W and N. Using the same compass setting, place the point of the compass on point H and draw an arc that intersects the ray. Label the intersection point S. Place the point of the compass at point N and draw an arc that intersects with the point W. Without changing the compass setting, put the point of the compass at point S and draw an arc that intersects the first arc. Label the intersection point L. Connect H and L. The angle should be the same as I.

mWIN is read “measure of angle WIN” congruent angles Angles that have the same measure. mWIN = mLHS WIN  LHS Notation: “Arc marks” indicate congruent angles. Notation: To write the measure of an angle, put a lowercase “m” in front of the angle bracket. mWIN is read “measure of angle WIN” ● L H S W I N

interior of an angle Angle Addition Postulate The set of all points between the sides of an angle If D is in the interior of ABC, then mABD + mDBC = mABC (part + part = whole) ● A B D C

A ray that divides an angle into two congruent angles. angle bisector A ray that divides an angle into two congruent angles. Example: UF bisects SUN; thus SUF  FUN or mSUF = mFUN ● S U N F

Constructing an Angle Bisector Draw an angle with sides at least 3“ long and label the vertex J Open the compass about 2“. Place the point of the compass on point J and draw an arc that intersects both sides. Label the intersection points K and L. Place the compass point on K and draw an arc in the interior of the angle. Repeat on point L. Label the intersection point M. Connect J and M. This is an angle bisector.

Drawing a Specific Angle Draw a ray at least 3“ long. Label the endpoint B. Line the center mark of your protractor at the endpoint and the 0º/180º mark along the ray. Count up from 0º along the edge of the protractor until you find 55º degrees. Make a mark on your paper at that point. Remove the protractor and connect the endpoint of the ray with the mark.