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Unit 1A – Angle Measure (Notes) Name: Objective(s): Key Concepts Date: Essential Question(s): Notes degree definition ray What does it look like? How is it named? Opposite ray = straight angle definition angle formal definition parts of an angle There are FOUR ways to name an angle: What does it look like? How is it named? How does an angle divide the coordinate plane? Page 1 478173003 Key Concepts Notes Example 1 a) Name all angles that have B as a vertex a) b) Name the sides of ∠5 b) c) Write another name for ∠6 c) d) Name the vertex of ∠4 d) e) Name the sides of ∠7 e) f) Write another name for ∠EBG f) Page 2 478173003 Key Concepts Notes Example 2 a) Name all angles that have W as a vertex a) b) Name the sides of 1 b) c) What are four other ways to write WYZ? c) Types or Classifications of Angles Right Acute Obtuse Congruent Angles Definition What do they look like? How is it written? Angle bisector Definition Page 3 478173003 Key Concepts Notes Example 3 a) Name two angles that are congruent a) b) Name two angles that are not congruent b) c) Name the straight angle c) Example 4 Given: and are opposite rays, and bisects a) If m <RQT = 6x + 5 and m <SQT = 7x – 2, find m <RQT. a) b) Find m <TQS if m <RQS = 22a – 11 and m <RQT = 12a – 8. b) Summary, Reflection, & Analysis Page 4 478173003 Unit 1A – Angle Measure Construction – Copy an Angle Name Date You can construct an angle congruent to a given angle without knowing the measure of an angle. Construction – Copy an Angle 1. Draw an angle on your paper and label it P on your paper. Below P, use a straightedge to draw a ray on your paper and label its endpoint T. 2. Place the tip of the compass at point P and draw a large arc that intersects both sides of P. Label the points of intersection Q and R. 3. Using the same compass setting, place the compass at point T and draw a large arc that intersects the ray. Label the point of intersection S. 4. Place the point of your compass on R and adjust so that the pencil tip is on Q. 5. Without changing the setting, place the compass at S and draw an arc to intersect the larger arc you drew in Step 3. Label the point of intersection U. 6. Use a straightedge to draw line TU. Conclusion: P _________ UTS Page 5 478173003 Unit 1A – Angle Measure Construction –Bisect an Angle Name Date You can construct the angle bisector of any angle without knowing the measure of the angle. Construction – Bisect an Angle 1. Draw an angle on your paper and label the vertex as point A. Put your compass at point A and draw a large arc that intersects both sides of A. Label the points of intersection B and C. 2. With the compass at point B, draw an arc in the interior of the angle. 3. Keeping the compass the same setting, place the compass at point C and draw an arc that intersects the arc drawn in Step 2. 4. Label the point of intersection point D. Draw line AD. Line AD is the bisector of A. Conclusion: mBAD _________ m DAC, therefore, BAD _________ DAC Page 6 478173003 Unit 1A -Section 4: Angle Measure Assignment #1 Name: ________________________ Date: ______________ Must show ALL Work For Exercises 1-10, use the figure to the right. Name the vertex of each angle. 1. 2. 3. 3. 4. 4. Name the sides of each angle. 5. 6. 7. Write another name for each angle. 8. 9. 10. For Exercises 11-15, use the figure to the right. Write another name for each angle. 11. 12. 13. 14. 15. Page 7 478173003 For Exercises 16 and 17, use the figure to the right and the given information. bisects , and and are opposite rays. 16. If and find the value of x 17. If find and For Exercises 18 -20, use the figure to the right and the given information. and are opposite rays, bisects and bisects 18. If 19. If 20. If and , find and , find and . , find A five-pointed star sticker is shown below right with vertices labeled. 21. Find and if . Page 8 478173003 Unit 1A -Section 4: Angle Measure Assignment #2 Name: __________________ Must show ALL Work For Exercises 1 - 5, use the figure to the right and the given information. and are opposite rays, bisects , and bisects . 1-4: Write another name for each angle. 1. 2. 3. 4. 5. Name all sets of congruent angles. 6. 7. If 8. If Page 9 . Explain why in complete sentences. and , find . . 478173003 For Exercises 9 – 12, use the figure to the right. 9. Name at least one right angle. 10. Name at least two different acute angles. 11. Name at least one obtuse angle. 12. Name two angles that make a right angle together. For Exercises 13 and 14, use the figure to the right and the given information. and are opposite rays, bisects , and bisects . 13. If . 14. If . Page 10 478173003