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1.6-1.7 Angles and Their Measures

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1.6-1.7 Angles and Their Measures

Geometry

Objectives:

- Use angle postulates
- Classify angles as acute, right, obtuse, or straight.

- 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.

- 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.

- Angles that have the same measure are called congruent angles.

50°

MEASURES ARE EQUAL

mBAC = mDEF

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).

- 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.

- If P is in the interior of RST, then
mRSP + mPST = mRST

- All angles are classified as acute, right, obtuse, and straight, according to their measures.

6 and 5 are also a linear pair

m5 = 50˚.