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Module Five Review
Please print this study guide prior to participating in the Module Five Review Session.
Slide Two: [5.01]
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Number of Sides
Polygon
Heptagon
Octagon
Nonagon
Decagon
Number of Sides
Slide Three: [5.01]
Definitions (Student Created)
Regular Polygon: ________________________________________________________________
Convex Polygon: ________________________________________________________________
Concave Polygon: _______________________________________________________________
Slide Four and Five:[5.01]
Property
Opposite sides are
parallel
Opposite sides are
congruent
Opposite angles are
congruent
Diagonal forms 2
congruent triangles
Diagonals bisect each
other
Diagonals are congruent
Diagonals bisect
opposite angles
All angles are right
angles
All sides are congruent
Diagonals are
perpendicular
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Kite
Slide Six:[5.02]
PQRS is a parallelogram.
1.
2.
3.
4.
If PS = 5, then QR = ______.
If m∠ S = 85, then m∠ R = ______.
If PT = 4.2, then PR = ______.
If PQ = 3x + 5 and SR = 5x – 7, find x.
Slide Seven and Eight:[5.03]
Recall the midpoint formula:
Prove the quadrilateral is a parallelogram by using Theorem 5-7; if the diagonals of a
quadrilateral bisect each other, then it is a parallelogram. (Hint: Use the Midpoint formula.)
Recall the distance formula:
Prove the quadrilateral is a parallelogram by using Theorem 5-8; if one pair of opposite sides of
a quadrilateral is both congruent and parallel, then it is a parallelogram.
Slide Nine:[5.04]
Answer the following questions with always, sometimes, or never.
1. A rectangle is a parallelogram.
2. The diagonals of a parallelogram are congruent.
3. A rectangle is a rhombus.
Match the properties with the appropriate figure(s).
Rhombus
Diagonals are congruent.
Diagonals bisect each other.
Rectangle
All four angles are equal.
Opposite sides are parallel.
Square
All four sides are equal.
Slide Ten:[5.05]
ABCD is a rectangle. Solve for x, if the measure of angle ABC is 6x + 18.
WXYZ is a square and the diagonals intersect at point P. If WY = 18, what is the length of PZ?
Slide Eleven:[5.06]
Solve for x.
Slide Twelve:[5.08]
True or false
A trapezoid is a parallelogram.
A midsegment of a trapezoid is found by getting the average of the top and bottom bases
In the example above you would solve by adding the top and bottom bases, then divide by 2 to
get the midsegment
Formula: base 1 + base 2 = midsegment
2
or
KL + JM = NO
2
 How much is segment NO?
 If the slope of midsegment NO is 2/3 what is the slope of segment KL?
Slide Thirteen:[5.08]
Let’s Practice  (using figures above)
1.) Using isosceles trapezoid ABCD, segment AB=3x and segment CD=x + 14. Solve for x
2.) In trapezoid EFGH angle H = 90 and angle E = 110. How much is angle G and F?
3.) In isosceles trapezoid ABCD, diagonal BD = 25, how much is diagonal AC?
4.) In isosceles trapezoid ABCD, if angle BAD = 68 degrees, how much is angle CDA?
Slide Fourteen:[5.09]
Indirect Reasoning: It is assuming the opposite of what you want to conclude
Indirect Proof: It is a proof by contradiction.
Steps to solving an indirect proof
1. Assume the conclusion is not true.
2. Reason logically by showing that the assumption leads to a contradiction of a known
fact by using definitions, postulates, previously proven theorems, or given information.
3. Conclude the assumption is false and the Prove statement is true.
Multiple choice: What is the first step of an indirect proof?
1.) The chair is green today.
A. The chair is green tomorrow.
B. The chair is not green today.
2.) Lines RP and ST are parallel.
A. Lines RP and ST are not parallel.
B. Lines RP and ST are perpendicular.
Slide Fifteen:
Use this space to write down any questions you may have so you won’t forget, or you can
take notes on here based on the questions asked by your classmates.