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. 174-5 # 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. 180-1 #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

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. 192-3 #1-11, 14-18 Other Suggested Exercises: p. 197-8 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.