1.4 Angles and Their Measures. Geometry Mr. Davenport Fall 2009. Standard/Objectives:. Performance Standard : Solve problems involving complementary, supplementary and congruent angles. Objectives : Use angle postulates Classify angles as acute, right, obtuse, or straight.
Performance Standard: Solve problems involving complementary, supplementary and congruent angles.
An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.
The angle that has sides AB and AC is denoted by BAC, CAB, A. The point A is the vertex of the angle.Using Angle Postulates
Name the angles in the figure: initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.
There are three different angles.
PQS or SQP
SQR or RQS
PQR or RQPEx.1: Naming Angles
You should not name any of these angles as Q because all three angles have Q as their vertex. The name Q would not distinguish one angle from the others.
mBAC = 50°.
Angles that have the same measure are called congruent angles. For instance, BAC and DEF each have a measure of 50°, so they are congruent.more . . .
MEASURES ARE EQUAL angles. For instance,
mBAC = mDEF
ANGLES ARE CONGRUENT
BAC DEFNote – Geometry doesn’t use equal signs like Algebra
“is congruent to”
“is equal to”
Note that there is an m in front when you say equal to; whereas the congruency symbol ; you would say congruent to. (no m’s in front of the angle symbols).
Consider a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 1-180.
The measure of AOB is equal to the absolute value of the difference between the real numbers for OA and OB.Postulate 3: Protractor Postulate
A point is in the interior of an angle if it is between points that lie on each side of the angle.
A point is in the exterior of an angle if it is not on the angle or in its interior.Interior/Exterior
If P is in the interior of points that lie on each side of the angle. RST, then
mRSP + mPST = mRSTPostulate 4: Angle Addition Postulate
VISION. points that lie on each side of the angle. Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°.
Find the angle of vision seen by the left eye alone.Ex. 2: Calculating Angle Measures
You can use the Angle Addition Postulate. points that lie on each side of the angle.Solution:
Two angles are adjacent angles if they share a common vertex and side, but have no common interior points.
Angles are classified according to their measure. Those measuring less than 90° are acute. Those measuring 90° are right. Those measuring between 90° and 180° are obtuse, and those measuring exactly 180° are straight angles.