Transcript Chapter 8.5 Notes: Use Properties of Trapezoids and Kites

Chapter 8.5 Notes: Use
Properties of Trapezoids and
Kites
Goal: You will use properties of trapezoids
and kites.
Trapezoids
• A trapezoid is a quadrilateral with exactly one pair
of parallel sides.
• The parallel sides are called the bases.
• A trapezoid has two pairs of base angles.
• The nonparallel sides are the legs of the trapezoid.
Ex.1: Show that ORST is a trapezoid.
• If the legs of a trapezoid are congruent, then the
trapezoid is an isosceles trapezoid.
• Theorem 8.14:
If a trapezoid is isosceles, then each pair of base
angles are congruent.
• Theorem 8.15:
If a trapezoid has a pair of congruent base angles,
then it is an isosceles trapezoid.
• Theorem 8.16:
A trapezoid is isosceles if and only if its diagonals
are congruent.
Ex.2: The stone above the arch in the diagram is an
isosceles trapezoid. Find mK , mM , mJ .
Ex.3: The top of the table in the diagram is an
isosceles trapezoid. Find mN , mO, mP.
• The midsegment of a trapezoid is the segment that
connects the midpoints of its legs.
• Theorem 8.17 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.
Midsegment = __________________________
Ex.4: In the diagram, MN is the midsegment of
trapezoid PQRS. Find MN.
Ex.5: In the diagram,HK is the midsegment of
trapezoid DEFG. Find HK.
Ex.6: Use the diagram of trapezoid EFGH.
a. If EG = FH, is trapezoid EFGH isosceles? Explain.
b. If mHEF  70 and mFGH  110 , is
trapezoid EFGH isosceles? Explain.
o
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Kites
• A kite is a quadrilateral that has two pairs of
consecutive congruent sides, but opposite sides are
not congruent.
• Theorem 8.18:
If a quadrilateral is a kite, then its diagonals are
perpendicular.
• Theorem 8.19:
If a quadrilateral is a kite, then exactly one pair of
opposite angles are congruent.
Ex.7: Find mD in the kite shown below.
Ex.8: In a kite, the measures of the angles are 3xo,
75o, 90o, and 120o. Find the value of x. What are the
measures of the angles that are congruent.
Ex.9: Find mC in the kite shown.