Download Introduction to Quadrilaterals_solutions.jnt

Algebra & Analytic Geometry
Name & Date
Coordinate Geometry - Introduction to Quadrilaterals
Directions: Draw at least two examples of each type of quadrilateral based on the given definition.
1) QUADRILATERAL: A polygon is a quadrilateral if and only if it has 4 sides.
2) PARALLELOGRAM: A quadrilateral is a parallelogram if and only if both pairs of its opposite sides are
parallel.
3) RHOMBUS: A quadrilateral is a rhombus if and only if its four sides are equal in length.
4) RECTANGLE: A quadrilateral is a rectangle if and only if it has four right angles.
5) SQUARE: A quadrilateral is a square if and only if it has four equal sides and four right angles.
6) KITE: A quadrilateral is a kite if and only if it has two distinct pairs of consecutive sides of the same length.
7) TRAPEZOID: A quadrilateral is a trapezoid if and only if it has at least one pair of parallel sides.
8) ISOSCELES TRAPEZOID: A trapezoid is an isosceles trapezoid if and only if it has a pair of base angles
equal in measure.
Directions: In 9-14, classify the polygon based only upon the markings given. Give the most specific
name.
9)
10)
11)
12)
13)
14)
15) Based on the markings only, please classify each figure below as specifically as you can. The diagrams are
NOT drawn to scale so be sure to consider the definitions when classifying quadrilaterals (don’t assume)!
16) In a rectangle, the length of one side is 8 less than triple the width. If the perimeter is 84, then find the
area of the rectangle. Be sure to draw and label a diagram as well as write and solve an equation below.
Directions: The slopes and the lengths of the sides of quadrilateral PQRS are provided in the table
below. Use the information to determine the type of quadrilateral that best matches the characteristics
of PQRS. You must draw and label a sketch and briefly describe your reasoning.
17)
Segment
Slope
Length
PQ
3/4
10
QR
-3/4
10
RS
15/8
17
SP
-15/8
17
18)
Segment
Slope
Length
PQ
-6
34
QR
1/6
43
RS
-6
34
SP
1/6
43
Segment
Slope
Length
PQ
3/5
12
QR
-5/3
12
RS
3/5
12
SP
-5/3
12
19)
20)
21)
Segment
Slope
Length
Segment
Slope
Length
PQ
2/3
7
PQ
3/7
18
QR
-1/8
7
QR
-5/7
43
RS
2/3
7
RS
3/7
27
SP
-1/8
7
SP
5/7
43
22)
23)
Segment
Slope
Length
Segment
Slope
Length
PQ
Undefined
17
PQ
3
5
QR
0
22
QR
1/3
9
RS
-5
20
RS
3
5
SP
0
35
SP
1/3
9
24) Quadrilateral ABCD has coordinates A (-2, 9), B (8, 8), C (7, -2) and D (-3, -1).
A) Construct ABCD in the coordinate plane.
B) Find the slope of each side.
C) Find the length of each side.
D) Quadrilateral ABCD is a
because
E) Construct AC and BD . These segments are called the diagonals on the quadrilateral.
F) Find the midpoints, lengths, and slopes of AC and BD . What can you conclude?