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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Warm-up Lesson: Cyclic Quadrilaterals Homework / Questions Clean-up. Warm-up. Define cyclic . Draw a triangle with your straightedge. With compass and straightedge: Find the circumcenter .

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Warm-up • Lesson: Cyclic Quadrilaterals • Homework / Questions • Clean-up

  3. Warm-up • Define cyclic. • Draw a triangle with your straightedge. • With compass and straightedge: • Find the circumcenter. • Circumscribe a circle around the triangle.

  4. When is a quadrilateral cyclic?

  5. Theorem • A quadrilateral is cyclic iff its opposite angles are supplementary.

  6. Proof, Part I Given: Cyclic quadrilateral ABCD. Prove:A is supplementary to C. Hints: draw the circle; use inscribed angles.

  7. Proof, Part II Given: In quadrilateral ABCD,A is supplementary to C. Prove: ABCD is cyclic. Proof sketch: Circumscribe a circle about ABC. (All triangles are cyclic.) D is either inside, on, or outside the circle. Prove by contradiction that D cannot be inside or outside the circle.

  8. Homework • Asg #85: • From Ch. 13, Lesson 1 (pp. 530-535): • Easy: 1-14. Med/hard: 46-48. • From Ch. 13, Lesson 2 (pp. 537-539): • Easy: 1-2, 6-12. Med: 29-31. • Bonus: Set III from Ch. 13, Lesson 1. • Due Friday, 6/7. • Final Exam Study Guide • Due the day of the final.

  9. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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