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6.4

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

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6.4

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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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