Trapezoids and KitesTrapezoids and Kites

TrapezoidsTrapezoids

A A trapezoid trapezoid is a quadrilateral with _______ is a quadrilateral with _______ _________ of _____________________ of ____________

____________. Draw below labeling ____________. Draw below labeling bases, two pairs of base angles, and legs.bases, two pairs of base angles, and legs.

onepair parallel

sides

base

base

leg leg

Isosceles TrapezoidsIsosceles Trapezoids

When is a trapezoid isosceles?When is a trapezoid isosceles?When the two legs are congruentWhen the two legs are congruent

What else will you know about an What else will you know about an isosceles trapezoid?isosceles trapezoid?Each pair of base angles is congruentEach pair of base angles is congruent

A trapezoid is isosceles if and only if its diagonals are _____________congruent

Example 1. Given a quadrilateral with coordinates O (0, 0), R (0, 3), S (2, 4), and T (4, 2). Draw on the coordinate plane below then prove that ORST is a trapezoid.

Example 2 Determine the missing angle measures for each trapezoid below.

Midsegment TheoremMidsegment Theorem

The ________________ of a trapezoid is The ________________ of a trapezoid is ____________ to each base and its length ____________ to each base and its length is _________ the _________ of the is _________ the _________ of the lengths of the two bases.lengths of the two bases.

Formula:

midsegment

parallelhalf sum

MN = 1/2(AB + CD)

Example 3 Determine the length of each midsegment below.

Example 4 Find the value of x.

KitesKites

A A kitekite is a quadrilateral that has __ _______ is a quadrilateral that has __ _______ of consecutive ______________ sides, of consecutive ______________ sides, but _____________ sides are NOT but _____________ sides are NOT _____________._____________.

2 pairscongruent

oppositecongruent

TheoremsTheorems

If a quadrilateral is a kite, then its diagonals If a quadrilateral is a kite, then its diagonals are _________________. are _________________. perpendicular

If a quadrilateral is a kite, then exactly ___ _________ of __________ angles are ___________.

1pair opposite

congruent

Example 5 EFGH is a kite. Find m<G.

Example 6 Find the side lengths of the kite.

Property Parallelogram Rectangle Rhombus Square Kite Trapezoid

All sides are congruent. AlwaysAlways AlwaysAlways

Both pairs of opposite sides are congruent.

AlwaysAlways AlwaysAlways AlwaysAlways AlwaysAlways

Exactly one pair of opposite sides are parallel.

AlwaysAlways

All angles are congruent. AlwaysAlways AlwaysAlways

Exactly one pair of opposite angles are congruent.

AlwaysAlways

Diagonals are perpendicular.

AlwaysAlways AlwaysAlways AlwaysAlways

Diagonals are congruent. AlwaysAlways AlwaysAlways

Both pairs of opposite sides are parallel.

AlwaysAlways AlwaysAlways AlwaysAlways AlwaysAlways

Diagonals bisect each other.

AlwaysAlways AlwaysAlways AlwaysAlways AlwaysAlways