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

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Presentation transcript:

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 Diagonals bisect each other

rhombus a parallelogram with four congruent sides.

rhombus a parallelogram with four congruent sides.

rectangle A parallelogram with four right angles.

rectangle A parallelogram with four right angles.

rectangle A parallelogram with four right angles.

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

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

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

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

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

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

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

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

The diagonals of a rhombus are perpendicular. Theorem 6.10

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

Theorem 6.11 The diagonals of a rectangle are congruent.

Checkpoint Find the value of x. rhombus ABCD 4. ANSWER 90 Use Diagonals Find the value of x. rhombus ABCD 4. ANSWER 90 rectangle EFGH 5. ANSWER 12 square JKLM 6. ANSWER 45 19