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Mastering Rectangles, Rhombuses, and Squares: Properties and Applications

Explore the properties of rectangles, rhombuses, and squares to solve geometric problems effectively. Understand how these special quadrilaterals relate to each other and learn to apply their unique characteristics in real-world scenarios. From constructing picture frames to verifying square properties, this comprehensive guide will enhance your geometric skills. Dive into the world of special parallelograms and enhance your problem-solving abilities with practical examples and helpful hints throughout. Start mastering rectangles, rhombuses, and squares today!

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Mastering Rectangles, Rhombuses, and Squares: Properties and Applications

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  1. Objectives Prove and apply properties of rectangles, rhombuses, and squares. Use properties of rectangles, rhombuses, and squares to solve problems.

  2. A second type of special quadrilateral is a rectangle. ______________– a quadrilateral with four right angles.

  3. Since a rectangle is a parallelogram by Theorem 6-4-1, a rectangle “inherits” all the properties of parallelograms that you learned in Lesson 6-2.

  4. Example 1: Craft Application A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.

  5. A rhombus is another special quadrilateral. A ______________– a quadrilateral with four congruent sides.

  6. Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

  7. Example 2A: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find TV.

  8. Example 2B: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find mVTZ.

  9. Helpful Hint Rectangles, rhombuses, and squares are sometimes referred to as special parallelograms. ____________ – a quadrilateral with four right angles and four congruent sides.

  10. Example 3: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

  11. Step 1 Show that EG and FH are congruent. Example 3 Continued

  12. Step 2 Show that EG and FH are perpendicular. Example 3 Continued

  13. Step 3 Show that EG and FH are bisect each other. Example 3 Continued

  14. Example 4 Given: PQTS is a rhombus with diagonal Prove:

  15. Check It Out! Example 4 Continued 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 7.

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