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.

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1 6 1 7 angles and their measures

1.6-1.7 Angles and Their Measures

Geometry


1 6 1 7 angles and their measures

Objectives:

  • Use angle postulates

  • Classify angles as acute, right, obtuse, or straight.


Using angle postulates

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

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.


1 6 1 7 angles and their measures

more . . .

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

50°


Note geometry doesn t use equal signs like algebra

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

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

Postulate 4: Angle Addition Postulate

  • If P is in the interior of RST, then

    mRSP + mPST = mRST


Classifying angles

Classifying Angles

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


1 6 1 7 angles and their measures

6 and 5 are also a linear pair

m5 = 50˚.


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