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Understanding Special Parallelograms: Rhombus, Rectangle, Square

Learn properties of parallelograms such as rhombus, rectangle, and square. Find sides, angles, and diagonal lengths in special quadrilaterals.

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Understanding Special Parallelograms: Rhombus, Rectangle, Square

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  1. 6.4 • EQ: What properties do we use to identify special types of parallelograms?

  2. Parallelogram (review) • Both pairs of opposite sides are parallel • Both pairs of opposite sides are congruent • Both pairs of opposite angles are congruent • Consecutive angles are supplementary • Diagonals bisect each other

  3. rhombus • a parallelogram with four congruent sides.

  4. rhombus • a parallelogram with four congruent sides.

  5. rectangle • A parallelogram with four right angles.

  6. A parallelogram with four right angles. rectangle

  7. A parallelogram with four right angles. rectangle

  8. square • A parallelogram with four congruent sides and four right angles.

  9. square • A parallelogram with four congruent sides and four right angles.

  10. SOLUTION a. AD = BC = 5 andAB = DC = 8. b. By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°. Example 1 Use Properties of Special Parallelograms In the diagram, ABCDis a rectangle. a. Find ADand AB. b. Find mA, mB, mC, and mD.

  11. Checkpoint 1. In the diagram, PQRSis a rhombus. Find QR, RS, and SP. ANSWER QR = 6,RS = 6, SP = 6 Use Properties of Special Parallelograms

  12. Rhombus Corollary • If a quadrilateral has four congruent sides, then it is a rhombus.

  13. Rectangle Corollary • If a quadrilateral has four right angles, then it is a rectangle.

  14. Square Corollary • If a quadrilateral has four congruent sides and four right angles, then it is a square.

  15. Checkpoint 2. rhombus ANSWER 3. square ANSWER Identify Special Quadrilaterals Use the information in the diagram to name the special quadrilateral.

  16. Theorem 6.10 • The diagonals of a rhombus are perpendicular.

  17. Example 3 Use Diagonals of a Rhombus ABCDis a rhombus. Find the value ofx. SOLUTION So, x = 90 – 60 = 30.

  18. Theorem 6.11 • The diagonals of a rectangle are congruent.

  19. Checkpoint 90 ANSWER 12 ANSWER 45 ANSWER Use Diagonals Find the value of x. 4. rhombusABCD 5. rectangleEFGH 6. squareJKLM

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