Quadrilaterals and Polygons: Squares, Rectangles and Rhombi

Warm-Up Icon Section Warm-Up


In this section, we are going to study three specific types of parallelograms. Before we do that, let’s review the properties we already know about parallelograms.

think icon Think & Click: Section Warm-Up

Now, you try. Complete the Think & Click activity by looking at the problem below, thinking about it, and then clicking on the question to reveal the solution.

Using parallelogram ABCD shown below, answer the following questions.

parallelogram ABCD with diagonals AC and DB intersecting at point M, height H is labeled

If AB measures 2x + 7 and DC measures 5x – 14, what is the value of x?
 

AB = DC

2x + 7 = 5x – 14

21 = 3x
x = 7
 

If DM measures 5a + 4 and DB measures 108, what is the value of a?
 

DM equals one-half DB; DM equals one-half the quantity 108 equals 54

5a + 4 = 54

5a = 50

a = 10
x = 37 

If the perimeter of the parallelogram is 100 feet, AB measures 2b + 5 and AD measures b + 3, what is the value of b?
 

2(b + 5) + 2(b + 3) = 100

4b + 10 + 2b + 6 = 100

6b + 16 = 100

6b = 84

b = 14
 

If the area of the parallelogram is 100 square feet, DC measures20 and the height is p – 2, what is the value of p?

b∙h = A

20(p – 2) = 100

20p – 40 = 100

20p = 140

p = 7
 

If angle DAB measures 122° and angle BCD measures (12x + 14)°, find the value of x.
 

12x + 14 = 122

12x = 108

x = 9
 

Find the distance between (-2, 4) and (3, -8).
 

d equals the square root of the sum of 3 minus negative 2, the quantity squared, and negative 8 minus 4, the quantity squared; d equals the square root of 5 squared plus the quantity negative 12, the quantity squared; d equals 25 plus 144; d equals the square root of 169; d equals 13
 

Find the slope of the line containing the points (3, 4) and (5, -4).
 

m equals the fraction negative 4 minus 4 all over the denominator 5 minus 3; m equals the fraction negative 8 over 2 equals negative 4 

If a line has a slope of the negative fraction 3 over 4, what is the slope of a line parallel to it? What is the slope of a line perpendicular to it?
 

Parallel lines have the same slope. m = the negative fraction 3 over 4

Perpendicular lines have negative reciprocal slopes. m = the fraction four over three