Download Discovering Properties of Trapezoids and Kites

Trapezoids and Kites: Properties 7-6 Notes
Name:__________________
This worksheet involves four new geometric definitions: a trapezoid, a kite, an isosceles trapezoid, and a midsegment. Write each
definition below backwards:
By definition, every trapezoid is a quadrilateral that has exactly one pair of parallel sides, and
so every _____________________ that ________________________________________________
___________________________________________________________________________ is a trapezoid.
By definition, every kite is a quadrilateral that has two pairs of consecutive congruent sides, and so every
_____________________________ that ________________________________________________________
____________________________________________________________________is a ________________.
consecutive,
congruent
sides
legs
By definition, every isosceles trapezoid is a trapezoid that has two congruent (but nonparallel) legs, and so
every ____________________ that _____________________________________________________________
is an _________________________________.
midsegment
By definition, every midsegment of a trapezoid is a line segment that has its endpoints at the midpoints
of the two (nonparallel) legs of a trapezoid, and so every _____________________________ that
____________________________________________________________________________________
________________________________________________ is a _______________________________.
Answer the questions about the figures below:
Trapezoid:
Isosceles Trapezoid:
Measure all four interior angles. Are any of the four angles congruent? ___
Measure the lengths of the two non-parallel sides. Are the two non-parallel
sides congruent? ___
Measure the lengths of the two parallel sides. Are the two parallel sides
congruent? _____
Draw the two diagonals. Measure their lengths, and the angle they form with
one another.
Are the diagonals congruent? _____ Are the diagonals perpendicular? _____
Isosceles Trapezoid:
Measure the two acute base angles. Compare their measures: The two acute
base angles of an isosceles trapezoid are _____________ to each other.
Measure the two obtuse base angles. Compare their measures: The two
obtuse base angles of an isosceles trapezoid are ___________ to each other.
Add the measures of one acute and one obtuse angle. What do you notice
about the sum? In an isosceles trapezoid, an obtuse base angle and an acute
base angle are always _______________________.
Draw the two diagonals. Measure their lengths, and the angle
they form with one another.
Are the diagonals congruent? ________
Are the diagonals perpendicular? ________
The diagonals of an isosceles trapezoid are ________________
to one another.
Measure the two legs (the non-parallel sides). Are they
congruent? _______
The two legs of an isosceles trapezoid are ____________.
Measure the lengths of the two parallel sides.
Are the two parallel sides congruent? _____
Kite:
Draw the two diagonals. Measure their lengths, and the angle
they form with one another.
Are the diagonals congruent? ________
Are the diagonals perpendicular? ________
The diagonals of a kite are _______________ to each other, and
they form four __________ triangles.
Kite:
Measure all four interior angles. Precisely two of them should be
congruent. Label them.
Are these two congruent angles formed by the pairs of congruent
sides, or are these two angles formed by the non-congruent sides?
In a kite, the two angles formed by the _______________ sides are
congruent to each other.
Midsegment of a Trapezoid:
Kite:
Examine the angles in the figure above. Highlight the diagonal that
bisects the opposite angles.
Is this diagonal joining the two pairs of congruent sides, or does it
join the two pairs of non-congruent sides?
In a kite, the diagonal joining the two pairs of __________________
sides bisects those two opposite angles.
Midsegment of a Trapezoid:
midsegment
Measure the top base. The top base measures _________cm.
Measure the bottom base. The bottom base measures
________cm.
Now, average the two bases. (Add them up and divide by
two). The average of the bases measures __________cm.
Now, measure the midsegment. The midsegment is _______
cm.
What do you notice about the length of the midsegment
compared to the average of the two bases?
The length of the midsegment of a trapezoid is equal to the
_________________________ of the two bases.
In other words, if the top base measures b1, and the bottom base
measures b2, then the formula for the length of the midsegment
is:
Measure all four angles along the left side of the figure, and
label the angle measures on the diagram.
What do you notice about all of the acute angles? All of the
acute angles on the left side of the figure are _______________
to each other.
What do you notice about all of the obtuse angles? All of the
obtuse angles on the left side of the figure are _____________
to each other.
Since the top and bottom bases of the trapezoid are parallel, and
the left side of the trapezoid is a transversal, and the
corresponding angles are congruent, what can we conclude
about the orientation of the midsegment? The midsegment is
___________________ to the two bases.
Repeat for the right side: measure all four angles. What do you
notice about all pairs of corresponding angles on the right side?