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OUTCOMES

You will be able to:

identify trapezoids by their properties. solve for missing information using trapezoid properties.Identify kites by their properties.Solve for missing information using kite properties.

Section 6.5 – Trapezoids and Kites

A trapezoid is a quadrilateral with _______________________.

The parallel sides are called the __________.

The nonparallel sides are called the _________.

exactly one pair of parallel sides

bases

legs

base

base

leg leg

Base Angles

Theorem 6.14: If a trapezoid is isosceles, then each pair of base angles is ___________.congruent

A

D

B

C

∠A ≅ ∠B, ∠C ≅ ∠D**Isosceles: two congruent side.**

Theorem 6.15: If a trapezoid has a pair of congruent base angles, then it is an ______________________.Isosceles Trapezoid

A

D

B

C

If ∠C ≅ ∠D, thenABCD is an isoscelesTrapezoid.

Theorem 6.16: A trapezoid is isosceles if and only if its diagonals are ________________.congruent

A

D

B

C

ABCD is an isoscelestrapezoidif and only if AC ≅ BD.

Examples

• Find the angle measures of ABCD.

L

J

M

K

Midsegment of a Trapezoid

Midsegment of a Trapezoid: the segment that connects the midpoint of its legs.

Theorem 6.17

MP = ½ (NO + LQ)

Kites and their Properties

• Kite: A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Theorems about Kites

Pythagorean Theorem• Reminder: Solve the sides of right triangles

with the Pythagorean Theorem.• a2 + b2 = c2

• The hypotenuse is always the longest side, across from the right angle.

a

b

c

Examples

Examples

Always, Sometimes, or Never???

never

sometimes

always

always

always

Example 5. Decide whether the following statements are always, sometimes, or never true. (a) Diagonals of a trapezoid are congruent. _____________ (b) Opposite sides of a rectangle are congruent. __________ (c) A square is a rectangle. _________ (d) All angles of a parallelogram are congruent. ______________ (e) Opposite angles of an isosceles trapezoid are congruent. __________ (f) The diagonals of a parallelogram are perpendicular. ______________

Sometimes

Always

Always

Sometimes

Never

Sometimes

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