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Understanding Quadrilateral Symmetry and Properties: A Detailed Algebra Review

In today's lesson, we will explore the concept of symmetry through the use of playing cards, separating them into piles based on their symmetry characteristics: point symmetry, line symmetry, both, and neither. We'll review key conjectures related to quadrilaterals, including Atticus' and Eva's conjectures pertaining to parallelograms. Homework will cover Chapter 7, focusing on selected exercises to strengthen understanding. Additionally, we'll practice proofs by demonstrating that a rectangle is indeed a parallelogram. Let’s engage in learning and sharing insights on geometry!

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Understanding Quadrilateral Symmetry and Properties: A Detailed Algebra Review

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Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #53: Ch. 6 Algebra Review: • Exercises 1-20. • Warm-up: Cards & Symmetry • Quadrilateral Conjectures & Proofs • Homework / Questions • Clean-up

  3. Warm-up Activity • Take out your deck of playing cards. • Separate them into 4 piles: • Cards that have point symmetry. • Cards that have line symmetry. • Cards that have both kinds of symmetry. • Cards that have neither. • Are there any that are almost symmetric? • What would you have to change to get symmetry?

  4. Conjectures • Atticus’ Conjecture: • The diagonals of a parallelogram divide the parallelogram into two congruent triangles. • Eva’s Conjecture: • If a quadrilateral has two pairs of equal opposite angles, it is a parallelogram. • I.e., if A = C and B = D, then ABCD is a parallelogram. • Conjecture (whose?): • All rectangles are parallelograms. • I.e., if quadrilateral ABCD is a rectangle, it is also a parallelogram.

  5. Homework • For Friday, 2/22: • Read & take notes on Ch. 7 L. 3. • For Monday, 2/25: • Asg#54: From Chapter 7, Lesson 1 (pp. 260-263): • Set I Exercises 1-15 • Set II Exercises 28-55 • Bonus: Set III.

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

  7. Proof Practice • Prove: A rectangle is a parallelogram. • Given: (1) ABCD is a rectangle. • Prove: ABCD is a parallelogram. • Proof: • Angles A, B, C, and D are right angles by definition (of rectangle). • A = C =90° and B = D = 90° by def. of right angle. • ABCD is a parallelogram (by Theorem since its opposite angles are equal.

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