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1.4 Angles and Their Measures

1.4 Angles and Their Measures. Geometry Mrs. Blanco. Standard/Objectives:. Objectives : Use angle postulates Classify angles as acute, right, obtuse, or straight.

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1.4 Angles and Their Measures

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  1. 1.4 Angles and Their Measures Geometry Mrs. Blanco

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

  3. 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. Angles name:by BAC, CAB, A. The point A is the vertex of the angle. Using Angle Postulates

  4. Name the angles in the figure: SOLUTION: There are three different angles. PQS or SQP SQR or RQS PQR or RQP Ex.1: Naming Angles BE CAREFUL: 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. Note: • The measure of A is denoted by mA. • mBAC = 50° or mA= 50° BAC and DEF each have a measure of 50°, so they are congruent.

  6. MEASURES ARE EQUAL mBAC = mDEF ANGLES ARE CONGRUENT BAC  DEF “is congruent to” “is equal to”

  7. 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. Interior/Exterior

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

  9. VISION. Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°. Find the angle of vision seen by the left eye alone. Ex. 2: Calculating Angle Measures

  10. Classifying Angles

  11. Ex. 3: Classifying Angles in a Coordinate Plane • Plot the points A(-2,4), B(3,5), C(6,-1), D(3,-4), E(-3,-3) and F(3,-1). • Use protractor to measure and classify the following angles as acute, right, obtuse, or straight. a. AFD b. AFE c. BFD d. BFC Need Graph Paper

  12. Solution:

  13. Ex. 4: Adjacent Angles Two angles are adjacent angles if they share a common vertex and side, but have no common interior points. PQS and SQR are adjacent

  14. Closure Question: • Describe how angles are classified. Angles are classified according to their measure. • Acute--less than 90° are acute. • Right-- measuring 90° • Obtuse-- between 90° and 180° • Straight--exactly 180°

  15. Extra Example—Angle Addition

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