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Learn to classify angles as acute, right, obtuse, or straight, understand angle postulates, measure angle degrees, identify vertices, and practice naming and classifying angles through practical examples and exercises. Explore how angles are classified based on their measures in a comprehensive geometry lesson.
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1.4 Angles and Their Measures Geometry Mrs. Blanco
Standard/Objectives: 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. Angles name:by BAC, CAB, A. The point A is the vertex of the angle. Using Angle Postulates
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.
Note: • The measure of A is denoted by mA. • mBAC = 50° or mA= 50° BAC and DEF each have a measure of 50°, so they are congruent.
MEASURES ARE EQUAL mBAC = mDEF ANGLES ARE CONGRUENT BAC DEF “is congruent to” “is equal to”
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
If P is in the interior of RST, then mRSP + mPST = mRST Postulate 4: Angle Addition Postulate
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
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
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
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°