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CLASSIFYING QUADRILATERALS
DAY 2
Bellwork
Please begin working on P 293 (60-63)
Using Algebra to Confirm the Name of a Quadrilateral
Determine the most precise name for a quadrilateral with points: A(-1,1), B(5,3), C(6,0), D(0,-2) Step 1: Find the slopes and side lengths of
each side. The slopes will show us how many sets of
parallel sides there are (slopes are the same). The slopes will also show us whether there are any right angles (slopes are opposite reciprocals)
Step 2: Find the length of each side using the distance formula.
Using Algebra to Confirm the Name of a Quadrilateral
Determine the most precise name for a quadrilateral with points: A(-1,1), B(5,3), C(6,0), D(0,-2)
Step 1: Find the Slopes of the sidesThe slopes of AB and CD
are the same. The slopes of BC and DA are the same. This means there are two sets of parallel sides and the
quadrilateral is some type of Parallelogram.
2 1
6 33
12 1
6 33
1
SlopeofAB
SlopeofBC
SlopeofCD
SlopeofDA
Using Algebra to Confirm the Name of a Quadrilateral
What else do the slopes tell us?
We now know that the quadrilateral belongs to the rectangle branch of the parallelogram family. What other shape besides a rectangle could it still be?A Square.
2 1
6 33
12 1
6 33
1
SlopeofAB
SlopeofBC
SlopeofCD
SlopeofDA
Two of the slopes are opposite reciprocals of the other two slopes. This means that the sides are perpendicular making 4 right angles. The shape must be some type of rectangle.
Using Algebra to Confirm the Name of a Quadrilateral
Step 2: Find the lengths of the Sides. This is done using the distance formula.
AB = CD and BC = DA, but they are not all the same length. This means the shape cannot be a square and is an ordinary rectangle.
2 2( 1 5) (1 3) 36 4 40
10
40
10
AB
BC
CD
DA
Practice Drawing Conclusions
Using the given information, identify the best name of the quadrilateral.
The quadrilateral is a parallelogram because it has two sets of equal slopes making the opposite sides parallel. It is not a rectangle because none the slopes are opposite reciprocals of each other, so there are no right angles. It is not a rhombus because all of the sides are not congruent.
A
D C
B 2
1
22
1
2
slopeofAB
slopeofBC
slopeofCD
slopeofDA
3
4
3
4
AB
BC
CD
DA
Practice Drawing Conclusions
Using the given information, identify the best name of the quadrilateral.
The quadrilateral is a Trapezoid because one set of slopes are equal meaning that one set of sides are parallel. It is not an isosceles trapezoid because none of the sides are congruent.
A
D C
B 1
2
1
3
slopeofAB
slopeofBC
slopeofCD
slopeofDA
10
2
5
3
AB
BC
CD
DA
Practice Drawing Conclusions
Using the given information, identify the best name of the quadrilateral.
The quadrilateral is a parallelogram because it has two sets of equal slopes making the opposite sides parallel. It is also a RECTANGLE because the slopes are not opposite reciprocals of each other, so there are right angles. It is not a rhombus or a square because all of the sides are not congruent.
A
D C
B 2
5
2
5
AB
BC
CD
DA
1
1
1
1
slopeofAB
slopeofBC
slopeofCD
slopeofDA
Homework
HW: P 339 (11,12) Find the most precise name of each shape without drawing a picture.
