1. Name the five properties of a parallelogram. ANSWER

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Presentation transcript:

1. Name the five properties of a parallelogram. ANSWER opp. sides , opp. sides , diags. bisect each other, opp. angles , consecutive angles are supp. = 2. Find x in the parallelogram. ANSWER 14

EXAMPLE 1 Use properties of special quadrilaterals For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. a. Q S SOLUTION a. By definition, a rhombus is a parallelogram with four congruent sides. By Theorem 8.4, opposite angles of a parallelogram are congruent. So, .The statement is always true. Q S

EXAMPLE 1 Use properties of special quadrilaterals For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. Q R b. SOLUTION If rhombus QRST is a square, then all four angles are congruent right angles. So, if QRST is a square. Because not all rhombuses are also squares, the statement is sometimes true. Q R

EXAMPLE 2 Classify special quadrilaterals Classify the special quadrilateral. Explain your reasoning. SOLUTION The quadrilateral has four congruent sides. One of the angles is not a right angle, so the rhombus is not also a square. By the Rhombus Corollary, the quadrilateral is a rhombus.

GUIDED PRACTICE for Examples 1 and 2 1. For any rectangle EFGH, is it always or sometimes true that Explain your reasoning. FG GH ? Sometimes; this is only true if EFGH is a square. ANSWER

GUIDED PRACTICE for Examples 1 and 2 2. A quadrilateral has four congruent sides and four congruent angles. Sketch the quadrilateral and classify it. ANSWER square

EXAMPLE 3 List properties of special parallelograms Sketch rectangle ABCD. List everything that you know about it. By definition, you need to draw a figure with the following properties: SOLUTION • The figure is a parallelogram. • The figure has four right angles. Because ABCD is a parallelogram, it also has these properties: • Opposite sides are parallel and congruent. • Opposite angles are congruent. Consecutive angles are supplementary. • Diagonals bisect each other. By Theorem 8.13, the diagonals of ABCD are congruent.

3. Sketch square PQRS. List everything you know about the square. GUIDED PRACTICE for Example 3 3. Sketch square PQRS. List everything you know about the square. ANSWER P Q S R 1. PQRS is a parallelogram, rectangle and a rhombus. 2. Opposite pairs of sides are parallel and all four sides are congruent. 3. All four angles are right angles. 4. Diagonals are congruent and bisect each other.

Daily Homework Quiz Name each type of quadrilateral (parallelogram, rectangle, rhombus, and square) for which the statement is true. 1. Both pairs of angles are congruent. ANSWER parallelogram, rectangle, rhombus, square. 2. The quadrilateral is equilateral. ANSWER rhombus, square.

Daily Homework Quiz 3. Given rhombus MNOP, find m NPO. ANSWER 48o

Daily Homework Quiz 4. Given rectangle QRST, find m RUS. ANSWER 128o