BellWork. OUTCOMES  You will be able to:  identify trapezoids by their properties.  solve for missing information using trapezoid properties.  Identify.

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Presentation transcript:

BellWork

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 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, then ABCD is an isosceles Trapezoid.

Theorem 6.16 : A trapezoid is isosceles if and only if its diagonals are ________________. congruent A D B C ABCD is an isosceles trapezoid if 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. a 2 + b 2 = c 2 The hypotenuse is always the longest side, across from the right angle. a b c

Examples

Always, Sometimes, or Never??? never sometimes 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 Sometimes Never Sometimes Exit Ticket