Discussion: With a partner, discuss what you believe a parallelogram is? Parallelogram Definition:

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1 Name: Ms. Ayinde Date: Geometry CC 4.2: Properties of Parallelograms Objective: To recognize and apply properties of sides, angles, and diagonals of parallelograms. To determine the area and perimeter of a parallelogram. Discussion: With a partner, discuss what you believe a parallelogram is? Parallelogram Definition: Using each of the accompanying diagram, list what you know about each parallelogram. 1. I know 2. I know 3. I know 4. I know 5. I know 6. I know

2 Properties of a Parallelogram: Interior Angle Sum = 360º Exterior Angle Sum = 360º Both pairs of opposite sides are congruent. Both pairs of opposite sides are parallel. Both pairs of opposite angles are congruent. Consecutive angles are supplementary. The diagonals bisect each other. The diagonals are not congruent. Practice:

3 Perimeter: The distance around a polygon; the sum of all the sides of a polygon. Area: The square units contained within a polygon. A = bh Example 1 b = base length h = height (altitude) *altitude: A line which passes through a vertex of a polygon and meets the opposite side at a right angle. Practice: Find the area and the perimeter for the following parallelograms. Round to the nearest tenth when necessary. 1. Area: Perimeter: 2. Area: Perimeter:

4 Homework Problem Set: Solve the following problems dealing with angles of polygons, area, perimeter, and parallelogram. Show your work for all of the following. 1. What is the measure, in degrees, of each exterior 2. angle of a regular hexagon? 1) 45 2) 60 3) 120 4) 135 In the diagram of parallelogram FRED shown below, ED is extended to A, and AF is drawn such that AF DF. If m R = 124, what is m AFD? 1) 124 2) 112 3) 68 4) 56 In the diagram below, ABCD is a parallelogram, 3. In the diagram below, parallelogram ABCD has 4. diagonals AC and BD that intersect at point E. The measure of an interior angle of a regular polygon is 120. How many sides does the polygon have? 1) 5 2) 6 3) 3 4) 4 Which expression is not always true? 1) DAE BCE 2) DEC BEA 3) AC DB 4) DE EB 5. Which statement is not always true about a 6. parallelogram? 1) The diagonals are congruent. 2) The opposite sides are congruent. 3) The opposite angles are congruent. 4) The opposite sides are parallel. Which statement is true about every parallelogram? 1) All four sides are congruent. 2) The interior angles are all congruent. 3) Two pairs of opposite sides are congruent. 4) The diagonals are perpendicular to each other.

5 7. 8. In the diagram below of parallelogram ROCK, m C is 70 and m ROS is 65. In the diagram below of parallelogram ABCD with diagonals AC and BD, m 1 = 45 and m DCB = 120. What is m KSO? 1) 45º 2) 110º 3) 115º 4) 135º 9. In the accompanying diagram of parallelogram 10. ABCD, diagonals AC and BD intersect at E, BE = 2 x, and ED = x What is the measure of 2? 1) 15º 2) 30º 3) 45º 4) 60º In the accompanying diagram of parallelogram ABCD, m B = 5x, and m C = 2x Find the number of degrees in D. What is the value of x? 1) 30 2) 30 3) 6 4) The diagram below shows parallelogram LMNO 12. with diagonal LN, m M = 118, and m LNO = 22. Determine and state the measure, in degrees, of an interior angle of a regular decagon. Explain why m NLO is 40 degrees.

6 Find the area and perimeter. As shown in the diagram below, the diagonals of parallelogram QRST intersect at E. If QE = x 2 + 6x, SE = x + 14, and TE = 6x 1, determine TE algebraically. 15. Find the area of ABCD. (Hint: You need to find the height of the parallelogram.) 16. Graph parallelogram ABCD with vertices A(1, 1), B(7, -7), C(8, 0), and D(2, 8). Determine the perimeter. (Hint: Use the distance formula.)