Quadrilaterals Worksheet With Answers Page 43
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502.
Determine which of the following statements is always, sometimes, or never true and
state a justification for each choice.
a) A square is a rectangle.
b) A rectangle is a square.
c) A rhombus is a square.
d) A rectangle has one pair of opposite sides parallel and congruent.
e) A diagonal bisects a pair of opposite angles in a rectangle.
f) Diagonal BD is drawn in square ABCD. ∠CAB and ∠DAC are complementary.
g) Diagonal AC is drawn in rhombus ABCD. ∆ADC is an isosceles triangle.
h) Diagonal BD is drawn in rhombus ABCD. m∠DAC = 45.
i) If a quadrilateral is a parallelogram, then it is a rhombus.
j) If a quadrilateral is a square, then it is a rhombus.
k) The diagonals of a rectangle are perpendicular.
l) The diagonals of a square intersect to form four non-overlapping congruent
triangles.
m) If one pair of consecutive angles in a quadrilateral are supplementary, then the
quadrilateral is a parallelogram.
n) A rhombus is equiangular (all angles are congruent).
o) A diagonal drawn in a parallelogram divides it into two congruent triangles.
3. The vertices of
ABCD are A(0,0), B(5,-4), C(9,1), and D(4,5).
a) Graph the parallelogram in the coordinate plane.
b) Identify the parallelogram as a rectangle, square, or rhombus.
c) Justify the identification.
4. Prove the theorem: Either diagonal of a rhombus bisects a pair of opposite
angles. (Optional)
5. Prove the theorem: If the diagonals of a parallelogram are congruent, then
the parallelogram is a rectangle. (Optional)
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