Quadrilaterals Lesson 6 1 Warmup Warmup Solve the

Quadrilaterals Lesson 6 -1

Warm-up

Warm-up �Solve the following triangles using the Pythagorean Theorem a 2 + b 2 = c 2 9 5 12 9 8 8√ 3

Warm-up �Find the missing point given the following information. 1. Point 1 (3, 8), Point 2 (5, 12), Midpoint (x, y) 2. Point 1 (-2, 5), Point 2 (3, -3), Midpoint (x, y) 3. Point 1 (2, 4), Point 2 (x, y), Midpoint (5, -1) 4. Point 1 (-1, 2), Point 2 (2, y), distance = 5

Parallelograms �A parallelogram is a quadrilateral with both pairs of opposite sides parallel

Properties of Parallelograms �Its opposite sides are congruent �Its opposite angles are congruent �Its consecutive angles are supplementary (add to 180°) �Its diagonals bisect each other. (Cut each other into 2 equal sections)

Let’s Practice �Find the value of each variable in the parallelogram.

Let’s Practice �Find the value of each variable in the parallelogram.

Types of Parallelograms �Rhombus – a parallelogram with four congruent sides. �Rectangle – a parallelogram with four right angles. �Square – a parallelogram four congruent sides and four right angles. �Rhombus Corollary – a quadrilateral is a rhombus if and only if it has four congruent sides. �Rectangle Corollary – a quadrilateral is a rectangle if and only if it has four right angles. �Square Corollary – a quadrilateral is a square if and only if it is a rhombus and a rectangle.

Special Parallelogram Properties �If a parallelogram is a rhombus, its diagonals are perpendicular. �If a parallelogram is a rhombus, each diagonal bisects a pair of opposite angles. �If a parallelogram is a rectangle, its diagonals are congruent.

Let’s Practice �Classify the special quadrilateral. Explain your reasoning. Then find the values of x and y.

Let’s Practice �Classify the special quadrilateral. Explain your reasoning. Then find the values of x and y.

Other Quadrilaterals �Trapezoid – a quadrilateral with exactly one pair of parallel sides. �Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Trapezoid Vocabulary �Base - the parallel sides are the bases. �Base Angles - in a trapezoid, the two angles that have that base as a side. �Legs – the non-parallel sides of a trapezoid. �Isosceles Trapezoid – a trapezoid where both legs are congruent. �Midsegment of a Trapezoid – the segment that connects the midpoints of the legs of a trapezoid.

Trapezoid Properties �For an isosceles trapezoid, each pair of base angles is congruent. �For an isosceles trapezoid, the diagonals are congruent. �Midsegment Theorem for Trapezoids – the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

Kite Properties �Its diagonals are perpendicular �Exactly one pair of opposite angles are congruent. �The diagonal between the non-congruent angles bisects the diagonal between the congruent angles.

Let’s Practice �Find “x”.

Let’s Practice

Let’s Practice