Module Five Review

Please print this study guide prior to participating in the Module Five Review Session.

Slide Two: [5.01]

Polygon / Number of Sides / Polygon / Number of Sides
Triangle / Heptagon
Quadrilateral / Octagon
Pentagon / Nonagon
Hexagon / Decagon

Slide Three: [5.01]

Definitions (Student Created)

Regular Polygon: ______

Convex Polygon: ______

Concave Polygon: ______

Slide Four and Five:[5.01]

Property / Parallelogram / Rectangle / Rhombus / Square / Trapezoid / Kite
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

Slide Six:[5.02]

PQRS is a parallelogram.

1. If PS = 5, then QR = ______.
2. If m∠ S = 85, then m∠ R = ______.
3. If PT = 4.2, then PR = ______.
4. 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).

RhombusDiagonals are congruent.

Diagonals bisect each other.

RectangleAll four angles are equal.

Opposite sides are parallel.

SquareAll 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 or KL + JM = NO

2 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. Reasonlogically 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.