# 1.6-1.7 Angles and Their Measures - PowerPoint PPT Presentation

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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. Using Angle Postulates.

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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.

### 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.

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

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

6 and 5 are also a linear pair

m5 = 50˚.