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Geometry 1-4 Angle Measure A. Definitions 1. Astronomer Claudius Ptolemy divided a __________ into 360 parts, which later became known as a degree. 2. A ray is part of a _________, it has one endpoint and extends indefinitely in one direction. D E Ray DE, written DE . 3. If you choose a point on a _______________, that point determines exactly two rays called opposite rays. C D E DC and DE are opposite rays 4. An angle is the intersection of two _______________ rays at a common endpoint. 5. The rays are called the sides of the angle. 6. The common endpoint is called the vertex. Side BA Vertex B B 2 Side BC E A ∠ABC ∠ _____ ∠ __ ∠ __ Call this: D C 7. Point D lies in the __________ of the angle. 8. Point E lies in the exterior of the angle. A G Example 1: a.) Using letters, name all the angles that have point B as a vertex. 5 c.) Write another name for ∠6 . ______ 6 7 D 3 ______, ______, ______, ______ b.) Name the sides of ∠5 . ______, ______ B E F 4 B. Angles 1. A right angle is ____ . 2. An acute angle is ____________ 90 . 3. An obtuse angle is greater than 90 , but less than _____. Example 2: Measure each angle and classify it as right, obtuse, or acute. a.) ∠TYV =______ __________ b.) ∠WYT =______ __________ c.) ∠TYU =______ ___________ U V T W Y S X 4. Angles that have the same measure are said to be congruent angles. Example 3: Find the value of x and ∠ABC . x = ______ ∠ABC =______ A C 12 x + 8 B 14 x − 12 D E 5. A ray that divides an angle into two __________ angles is called an angle bisector. Example 4: SV is an angle bisector of ∠RST , find x and m∠RST R S x = ____ m ∠RST =_______ HW: Geometry, Sec 1-4 p. 34-36 13-39 odd, 42 - 43, 50 -66 all 6x + 2 V 9 x − 13 T