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Lesson 7-8 Quadrilateral Applications
Level
1)
Blast from the PAST
In ∆ ABC, find x given that DE||BC, AD = 3, DE= 4 and DB = 6, find BC.
2) Find the ordered pair of the point that partitions the directed line segment FX into a 1:3
ratio where F (-4, -2) and X (4, 10).
3) Which is the scale factor for the dilation
of the resulting image being triangle ABC?
1)
3)
PQ
AB
AC
PQ
2)
AB
PQ
PR
4) AC
Level
Quadrilateral properties
____1) Which statements describe the properties of a rhombus?
a. The diagonals are perpendicular.
b. The diagonals are congruent.
c. The diagonals bisect each other.
d. The diagonals bisect the angles
Choose:
1) a,b,c and d
2) a,c and d
3) a and c
4) b and d
____2) Which property is not true for all parallelograms?
1.
2.
3.
4.
Opposite angles are congruent.
Consecutive angles are supplementary.
Opposite sides are congruent.
Diagonals are congruent.
____3) A parallelogram must be a rectangle if the
1.
2.
3.
4.
diagonals are perpendicular
opposite angles are congruent
diagonals are congruent
opposite sides are congruent
____4) Which quadrilateral has diagonals that always bisect its angles and also bisect each
other?
1.
2.
3.
4.
rhombus
rectangle
parallelogram
isosceles trapezoid
____5) Which quadrilateral has perpendicular diagonals which do not bisect each other?
1.
2.
3.
4.
rhombus
rectangle
kite
isosceles trapezoid
Level
Euclidean proofs
1) Given: Trapezoid ABCD with AB || DC
Prove: CED ~ AEB
Statements
1) Trapezoid
ABCD with AB || DC
Reasons
1) Given
2)
Statements
1)
Reasons
1) Given
Level
Coordinate geometry proof
Given: Quadrilateral FGHJ with F (-1, 5), G (3,3) H (6, -4)
and J (2, -2)
Prove: FGHJ is a parallelogram but NOT a rectangle.
Write out formulas, label calculations and include a conclusion.
Level
APPLY the quadrilateral properties
1) The diagonals of a rhombus are 12 and 24. Find the perimeter of the rhombus in simplest
radical form.
2) The measures of angles A and B of parallelogram ABCD are in the ratio of 3:7. Find the
measure of the larger angle.
3) EF is the median (mid-segment) of trapezoid ABCD.
BC = 2x - 8 and AD = 3x + 5 and EF = 16. Find BC.
4) a) If AC= 20 and BE = 12, find BC in simplest radical form .
o
b) If mABC  100 , find the measure of angle BAE.
Level
Polygon calculations
1) What is the total sum measure of all interior angles of a regular 20-gon?
2) What is the number of sides of a regular polygon if the sum of the measures of the
interior angles is 2340˚?
3) What is the number of sides of a regular polygon if each exterior angle measure 36˚?
4) What is the sum of the measures of the exterior angles of a dodecagon?