Download 6.6 Trapezoids and Kites - Cardinal O'Hara High School

6.6 Trapezoids and Kites
• A trapezoid is a quadrilateral with exactly one pair of
parallel sides.
• The parallel sides of a trapezoid are called bases.
• The nonparallel sides are called legs.
• Two angles that share a base of a trapezoid are called
base angles.
• An isosceles trapezoid is a trapezoid with legs that are
congruent.
Theorem 6.19
• If a quadrilateral is an isosceles trapezoid, then
each pair of base angles is congruent.
Finding Angle Measures in Trapezoids
• CDEF is an isosceles trapezoid and the measure of
angle C = 65. What are the measures of angle D,
angle E, and angle F?
mC  mD  180
65  mD  180
mD  115
mC  mF  65
mD  mE  115
Theorem 6.20
• If a quadrilateral is an isosceles trapezoid, then
its diagonals are congruent.
Midsegment of a Trapezoid
• The midsegment of a trapezoid is the segment
that joins the midpoints of its legs.
– Is parallel to the bases.
– The length of the midsegment is half the sum of the
lengths of the bases.
Kites
• A kite is a quadrilateral with two pairs of
consecutive sides congruent and no opposite
sides congruent.
Theorem 6.22
• If a quadrilateral is a kite, then its diagonals are
perpendicular.
Finding Angle Measures in Kites
• Quadrilateral DEFG is a kite. What are the
measures of angle 1, angle 2, and angle 3?
m1  90
90  m2  52  180
142  m2  180
m2  38
m3  52
Concept Summary
More Practice!!!!!
• Homework – Textbook p. 394 – 395 #7 –
36 ALL.