1.6-1.7 Angles and Their Measures

1. 1.6-1.7 Angles and Their Measures Geometry

2. Objectives: • Use angle postulates • Classify angles as acute, right, obtuse, or straight.

3. 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.

4. 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.

5. more . . . • Angles that have the same measure are called congruent angles. 50°

6. 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).

7. 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.

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

9. Classifying Angles • All angles are classified as acute, right, obtuse, and straight, according to their measures.

12. 6 and 5 are also a linear pair m5 = 50˚.