1. Geometry/Trig Name: __________________________
Unit 5 Study Guide Date: ___________________________
Section 5-1
Definitions: Parallelogram
Theorems:
5-1: Opposite sides of a parallelogram are congruent.
5-2: Opposite angles in a parallelogram are congruent.
5-3: Diagonals of a parallelogram bisect one another.
Know How To: set up algebraic equations by applying properties of parallelograms.
Suggested Exercises:
p. 168 #1-14
p. 169 #1-10
p. 170 #19-28
Section 5-2
Five ways to prove that a quadrilateral is a parallelogram (You will have to list these on your test.)
1. If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram (definition of a parallelogram).
2. If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
3. If one pair of opposite sides are both congruent and parallel, then the quadrilateral is a parallelogram.
4. If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
5. If the diagonals bisect one another, then the quadrilateral is a parallelogram.
Know How To: determine and prove (informally) that a quadrilateral is a parallelogram.
Suggested Exercises:
p. 173 #1-11
p # 1-10, 19-22
Section 5-3
Theorems:
5-8: If two lines are parallel, then all points on one line are equidistant from the other lines.
5-9: If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
5-10: A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
5-11: The segment that joins the midpoints of two sides of a triangle
1. is parallel to the third side.
2. is half the length of the third side.
Know How To: apply these theorem by setting up and solving algebraic equations.
Suggested Exercises:
p. 179 #2-6 p #1-17
Section 5-4
Definitions: Rectangle, Rhombus, Square
Properties of Special Parallelograms: Refer to property chart from 5.4 Exploration note pages.
Know How To: Classify a give quadrilateral, apply properties of special quadrilaterals by setting up and solving algebraic equations.
Suggested Exercises:
p. 187 #1-16

2. Geometry/Trig Name: __________________________
Unit 5 Study Guide – page 2 Date: ___________________________
Section 5-5
Definitions: Trapezoid, Base, Leg, Isosceles Trapezoid, Median of a Trapezoid
Theorems:
5-18: Base angles of an isosceles triangle are congruent.
5-19: The median of a trapezoid
1. is parallel to the bases.
2. has the length equal to the average of the base lengths.
Know How To: Determine whether a given quadrilateral is a trapezoid; determine whether a trapezoid is isosceles; calculate the length of the median of a trapezoid; apply theorem 5-19 by setting up and solving algebraic equations.
Suggested Exercises:
p. 192 C.E #1-11
p #1-11, 14-18
Other Suggested Exercises:
p Chapter Review #1-8, 13-16, 19-22
p. 199 Chapter Test (not 10-11)
Additionally: There will be problems on the test that involve systems of equations and factoring.