Download A quadrilateral that has one set of parallel sides is called a . For this

Trapezoids
A quadrilateral that has one set of parallel sides is called a
___________________.
For this picture, side AD and side BC (the parallel sides) are called the
________________.
Side AB and Side CD are called the ____________.
A trapezoid has two sets of __________ angles. In this picture _____ and
_____are one set of these, and angles _______ and ________ are the
other set.
The sum of the interior angles of a trapezoid is ____________.
For the picture above, m<a + m<b = ___________, and the m<c +m<d =
_________ because when two parallel lines are cut by a transversal,
______________ angles are _________________.
If AB = CD in the picture above, then the trapezoid is called an _________
trapezoid.
If one of the legs of a trapezoid is perpendicular to both bases, then the
trapezoid is called a _______________ trapezoid.
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Isosceles Trapezoid
Suppose you are given isosceles trapezoid ABCD with AB congruent to CD.
A line segment drawn with endpoints on each base, that is perpendicular to both bases,
is called an _____________ of the trapezoid. In the next picture, two altitudes, AE and
CF, will be drawn from base AC to base BD.
<AEF, <AEB, <CFD, and <CFE are right angles because of the definition of
______________________. Since < AEF and <CFE are supplementary consecutive
angles in quadrilateral ACFE, then AE is ____________to CF. Since AC II EF and AE
II CF, then quadrilateral ACFE is a _________________ because of the definition of a
parallelogram. Since ACFE is a parallelogram then AE = ______ because the opposite
sides of a parallelogram are ___________. (mark on picture above).
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Now, because of the angles and sides congruent in the picture above, triangle
________ is congruent to ___________ because of the _________ congruence
postulate.
Since these triangles are congruent, then <B must be congruent to __________
because corresponding parts of congruent triangles are congruent. Also, <BAC and
<ACD are going to be congruent. (why) Therefore, in an isosceles trapezoid, we have
proven that the base angle pairs of an isosceles triangle are ___________________.
Copy theorem 6-14 from Pg. 321 in the textbook below.
______________________________________________________________________
______________________________________________________________________
.
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In this isosceles trapezoid, we are going to draw diagonals AD and BC.
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Notice the two overlapping traingles ABD and CDB. Suppose we draw the two below.
AB = CD because of the definition of an _________ trapezoid. BD is equal to BD
because of the _____________ property. Furthermore, <ABD is congruent to <CDB
because the ________ angles of an isosceles trapezoid are congruent (proved on last
page). Mark the congruent parts discussed in the picture above.
Triangle ABD≅∆CDB because of the ________congruence postulate. Therefore,
AD≅BC because corresponding parts of congruent triangles are congruent. Since AD
and BC are the diagonals of the isosceles triangle, this proves that the diagonals of an
isosceles triangle are _____________.
Copy theorem 6-15 from Pg. 321 below
______________________________________________________________________
______________________________________________________________________
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Medians of a Trapezoid
A line that connects the midpoint of the legs of any trapezoid is called the
____________ of the trapezoid. Draw median EF in trapezoid ABCD above.
Which two sets of segments would be congruent with each other.
__________________
__________________
Theorem 6-16 says the median has two special properties.
1) _____________________________________
2) _____________________________________
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Homework: Pg. 325 # 5-10, 16-28 and guided practice problems on this page #4-24 all
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