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Understanding Angles and Rays: Concepts and Exercises

Dive into the world of geometry by exploring angles, rays, and their properties. This worksheet covers fundamental concepts such as angle measurement, opposite rays, and angle bisectors. Students will classify angles as right, acute, or obtuse while practicing with examples. Solve problems involving ray measurements and relationships between angles. Prepare to ask questions and clarify any doubts regarding concepts from sections 1-4. Perfect for reinforcing understanding of geometric principles and honing problem-solving skills.

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Understanding Angles and Rays: Concepts and Exercises

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  1. Get out your worksheets from yesterday. . . be ready to ask any questions

  2. Section 1-4: Angle Measure

  3. Ray E F G Has one endpoint and extends forever in the other direction Opposite rays Q P R Share an endpoint and continue in opposite directions. Opposite rays are collinear.

  4. Angles Are created by 2 non-collinear rays that have a common endpoint. Are made up of sides and a vertex. side AB B 4 vertex A A C side AC

  5. Angles CONT'D Angle Bisector – a ray that divides an angle into 2 congruent angles. Congruent angles – have the same measurement.

  6. Example 1 Example 2 S R T E 3 1 D 2 P Q A B C • Name all angles that have R as a vertex. • b. Name the sides of 1 • Classify each angle as right, acute or obtuse. • ABD • DBC • EBC

  7. Refer to the figure • Name the vertex of 4. • Name the sides of BDC. • Write another name for DBC. B A 4 3 1 2 C D • Classify each angle as right, acute or obtuse. • MPR • RPN • NPS N M S P R

  8. QS bisects PQT, and QP and QR are opposite rays. • If m PQT = 60 and m PQS = 4x + 14, find the value of x. • If m PQS = 3x + 13 and m SQT = 6x – 2, find m PQT T S` Q P R

  9. BA and BC are opposite rays, BF bisects CBE, and BD bisects ABE. • If m EBF = 6x + 4 and m CBF = 7x – 2, find m EBC • If m 1 = 4x + 10 and m 2 = 5x, find m 2. • If m 2 = 6y + 2 and m 1 = 8y – 14, find m ABE. • Is DBF a right angle? Explain. E D F 2 3 1 4 B A C

  10. ASSIGNMENT pg. 34 12-38 evens

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