Angles and Their Measures

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Presentation transcript:

1.6-1.7 Angles and Their Measures Geometry

Standard/Objectives: Performance Standard: Solve problems involving complementary, supplementary and congruent angles. Objectives: Use angle postulates Classify angles as acute, right, obtuse, or straight.

Using Angle Postulates 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.

Ex.1: Naming Angles Name the angles in the figure: SOLUTION: There are three different angles. PQS or SQP SQR or RQS PQR or RQP 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.

more . . . 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. 50°

Note – Geometry doesn’t use equal signs like Algebra MEASURES ARE EQUAL mBAC = mDEF ANGLES ARE CONGRUENT BAC  DEF “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).

Interior/Exterior 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.

Postulate 4: Angle Addition Postulate If P is in the interior of RST, then mRSP + mPST = mRST

Classifying Angles Angles are classified as acute, right, obtuse, and straight, according to their measures. Angles have measures greater than 0° and less than or equal to 180°.

Solution: Begin by plotting the points. Then use a protractor to measure each angle. Two angles are adjacent angles if they share a common vertex and side, but have no common interior points.

6 and 5 are also a linear pair m5 = 50˚.

Note: The measure of A is denoted by mA. The measure of an angle can be approximated using a protractor, using units called degrees(°). For instance, BAC has a measure of 50°, which can be written as mBAC = 50°. B A C

Ex. 3: Classifying Angles in a Coordinate Plane Plot the points L(-4,2), M(-1,-1), N(2,2), Q(4,-1), and P(2,-4). Then measure and classify the following angles as acute, right, obtuse, or straight. LMN LMP NMQ LMQ

Solution: Begin by plotting the points. Then use a protractor to measure each angle.