Download C 29

Level C Lesson 29
Quadrilateral Attributes
In lesson 29 the objective is, the student will be able to identify different types of
quadrilaterals based on attributes, and draw examples of quadrilaterals that do and do not
belong to subcategories.
The skills students should have in order to help them in this lesson include knowledge of
polygons and quadrilaterals.
We will have three essential questions that will be guiding our lesson. Number 1, explain
the difference between a rectangle and a square. Number 2, how do you know if a
quadrilateral is a parallelogram? And number 3, sketch an example of a quadrilateral that
is not a rectangle, square, parallelogram, rhombus or trapezoid.
The SOLVE problem for this lesson is, The Flannery family is putting an in-ground pool
in their backyard. The pool company told them that they could use any shape
quadrilateral they wanted for the pool. Mrs. Flannery told her daughter, Chloe, that the
pool was going to have two right angles and one pair of parallel sides. What quadrilateral
will the shape of the pool represent?
We are going to begin by Studying the Problem. First we want to identify where the
question is located within the problem and we will underline the question. What
quadrilateral will the shape of the pool represent? Now that we have identified the
question we want to put this question in our own words in the form of a statement. This
problem is asking me to find the quadrilateral that represents the shape of the pool.
During this lesson we will learn how to classify quadrilaterals based on attributes. We
will use this knowledge to complete this SOLVE problem at the end of the lesson.
Throughout this lesson students will be working together in cooperative pairs. All
students should know their role as either Partner A or Partner B before beginning this
lesson.
First you are going to do an activity with your class called getting into groups. You will
begin the lesson by sorting students into groups based on a certain characteristic. Go
ahead and do that now. How are your sorted? By shirt color, hair color, pant color, type
of shoes, or are you sorted in another way, talk about this with your class. Now let’s do it
again! You want to be sorted in a different way. How are you sorted this time? Talk
about it again as a class. Now that you have had a discussion as a class about the
characteristics, that were used to sort you into groups.
We are going to take a look at several shapes. We need to begin by cutting out the shapes
on the Copy Master that is provided by your teacher. We don’t want to cut directly on
the lines, because we don’t want to cut off the congruency marks on the shapes. Once all
of your shapes are cut out, Partner A, set your shapes aside, and Partner B, keep your
shapes out. You should have a group of shapes that is the same as what you see here.
We can use characteristics of the shapes to sort and organize them. Describe some
characteristics that we can use to sort the shapes. We could sort the shapes by right
angles or no right angles, congruent sides, or parallel sides. Take a look at the group of
shapes. We see that several of the shapes have right angles, parallel sides and congruent
sides. I’m sure that you could come up with other characteristics that we could use to
classify our shapes. Each of the shapes that we cut out is called a Quadrilateral. Create a
definition for quadrilateral based on your observation of the shapes. A quadrilateral is a
closed figure that has four sides. Explain why each of the shapes are quadrilaterals. Each
shape has four sides and is a polygon. We have many different types of quadrilaterals.
We will learn how to classify them using attributes. Attributes are what help you
distinguish the shapes from each other. One of the attributes we will be looking at is
congruent sides.
Take a look at Figure A. Figure A has four congruent sides. What does it mean if sides
are congruent? It means that the sides are exactly the same length. Identify any
markings on Figure A. We see that there are four lines, one on each side of Figure A.
What do you think those lines mean? In a shape, the sides that have the same number of
lines through them are congruent. Remember that congruent means that the sides are
exactly the same length.
Take a look at Figure D. How many sides are congruent? All four sides are congruent.
We see that each of the sides has one line through it. This line means that the sides are
congruent.
Now let’s take a look at Figure I. How many sides are congruent? There are two
different sets or pairs of sides. The sides with one line are congruent to each other. The
sides with two lines are congruent with each other. Another attribute we will look at is if
quadrilaterals have right angles. Identify a quadrilateral that has a right angle. Figure A,
C, I, and J all have right angles. How do you know that a quadrilateral has a right angle?
it makes an “L” shape and has a square inside of it. Take the corner of a piece of paper,
which is a right angle, and see if it fits perfectly into the corner of Figure A. We can see
that the corner of our paper fits perfectly into the corner of Figure A. This is one way to
check and see if an angle is a right angle. What other ways could we check an angle to
see if it is a right angle? The corner should form a perfect capital letter “ L.” Put a corner
of a sticky note or an index card in it to test the angle. Now let’s draw a right angle for
Question 6. To draw a right angle, we start by drawing the two sides. To check to see
that our angle is drawn correctly, we can take the corner of a piece of paper and see if it
fits perfectly into the corner of our drawing. Last we draw a little square in the corner to
represent that this is a right angle. So far we have talked about congruent sides and right
angles. The last attribute we will look at will look at is parallel sides. What is the
meaning of parallel sides? They are sides that could go on forever but will never touch or
intersect. For example, the two sides of railroad or roller coaster tracks always have to be
the same distance apart.
Now that we have talked about the three attributes, congruent sides, right angles and
parallel sides, we are going to take a look at a graphic organizer. The graphic organizer
on Student page two hundred seventy eight shows how to sort quadrilaterals based on the
attributes we’ve talked about in this lesson. Let’s start by determining which of the
shapes are quadrilaterals. Looking at the shapes we can see that they are all
quadrilaterals, because they are four-sided, closed figures.
Let’s take a look at the next box on the organizer. First we will look at Parallelograms.
A Parallelogram is a quadrilateral with two sets of parallel and congruent sides. We
know that all of the shapes that we have are quadrilaterals. We need to look for the
attributes of parallel and congruent sides. Explain how you can identify congruent sides.
We need to look for the lines on the sides to show that they are congruent. How many
sets, or pairs, of parallel sides must a quadrilateral have in order to be a parallelogram?
The definition tells us, it must have two sets of parallel sides. Now separate the shapes
that have two sets of congruent sides. Looking at the shapes we can see that shape A, C,
D, E, G, and I have two sets of congruent sides. Let’s take these shapes away from the
others to study them more carefully. Are the pairs of congruent sides also parallel?
Explain. Yes, I can put my pencils over the sides, and they could go forever without
touching, similar to railroad tracks. Are all of these parallelograms still quadrilaterals?
Yes, because they have four sides. Are all parallelograms quadrilaterals? Yes, all
parallelograms are quadrilaterals, because they are closed figures with four sides. Are all
quadrilaterals parallelograms? No. A trapezoid is a quadrilateral but it does not satisfy
the definition of a parallelogram. A trapezoid does not have two sets of parallel and
congruent sides.
Now let’s talk about rectangles. A rectangle is a parallelogram with two sets of
congruent sides and four right angles. Explain which shapes we should look at to identify
the rectangles. We need to consider only the parallelograms because the definition tells
us that rectangles are parallelograms. Which shapes do you think are rectangles? Shape
I, C, and A are all rectangles. They are parallelograms with four right angles. How are
the rectangles still parallelograms? They have two sets of parallel and congruent sides.
We will take these three shapes and place them under Rectangles, as all three are
parallelograms with two sets of congruent sides and four right angles.
Now let’s talk about which shapes would be classified as a Rhombus. A Rhombus is a
parallelogram with four congruent sides. Explain which shapes we should look at to
identify the rhombuses. We need to consider only the parallelograms because the
definition tell us that they are parallelograms. Which shapes do you think are
rhombuses? Shape A, and D are both rhombuses. They are parallelograms with four
congruent sides. Let’s take shapes A and D and place them under Rhombus. Explain
how these rhombuses are still parallelograms. They both have two sets of parallel and
congruent sides.
Now let’s talk about the shapes that are Square. The definition of a square is a
parallelogram with four congruent sides and four right angles. Explain which shapes we
should look at to identify the squares. We need to consider only the parallelograms
because the definition tells us that squares are parallelograms. Which shapes do you
think are squares? Shape A is a square. Figure A is a parallelogram with four congruent
sides and four right angles. Let’s take shape A and place it under the definition for a
square. Explain how this square is still a parallelogram. We still have two sets of
parallel and congruent sides. Explain how this square is still a rectangle. It is a
parallelogram with two sets of congruent sides and four right angles. And explain how
this square is still a rhombus. It is a parallelogram with four congruent sides.
Now let’s talk about those shapes that are Trapezoids. The definition of a trapezoid is a
quadrilateral with one set of parallel sides. Explain which shapes we should look at to
identify the trapezoids. We need to consider only the shapes that were NOT
parallelograms because a trapezoid has only one set of parallel sides, where a
parallelogram has two sets of parallel sides. We can remove all of the parallelograms
from our group of shapes when we are trying to see which of the remaining shapes are
trapezoids. Looking at the shapes that are not parallelograms, which ones do you think
are trapezoids? Shapes B, H and J are trapezoids. They each have one set of parallel
sides. Let’s take these shapes and place them under Trapezoid. Are trapezoids still
quadrilaterals? Yes, because they have four sides. Are the trapezoids rectangles? No,
because they do not have four right angles and two sets of congruent sides.
Are there any shapes left in the quadrilateral area? Yes, there are two shapes left, shapes
F and K. What do you think this means? These figures are quadrilaterals because they
have four sides, but they do not fit in any of the other categories.
So let’s summarize what we’ve done with these shapes. The shapes all started at the top
as quadrilaterals. As the arrows move down on the graphic organizer, so do the shapes.
Some shapes moved down to parallelograms and didn’t stop there. They also moved
down to rectangle, rhombus or square. Some of the shapes have many names. The best
name for a shape is the category that it ended up in, although it can be called anything
that was connected with an arrow above it.
We are now going to go back to the SOLVE problem from the beginning of the lesson.
The Flannery family is putting an in-ground pool in their backyard. The pool company
told them that they could use any shape quadrilateral they wanted for the pool. Mrs.
Flannery told her daughter, Chloe, that the pool was going to have two right angles and
one pair of parallel sides. What quadrilateral will the shape of the pool represent?
At the beginning of the lesson we Studied the Problem. We underlined the question,
what quadrilateral will the shape of the pool represent? And put this question in our own
words in the form of a statement. This problem is asking me to find the quadrilateral that
represents the shape of the pool.
We will now Organize the Facts. We will start by identifying the facts. The Flannery
family is putting an in-ground pool in their backyard, fact. The pool company told them
that they could use any shape quadrilateral they wanted for the pool, fact. Mrs. Flannery
told her daughter, Chloe, that the pool was going to have two right angles, fact, and one
pair of parallel sides, fact. What quadrilateral will the shape of the pool represent? Now
that we have identified the facts, we want to eliminate the unnecessary facts. These are
the facts that will not help us to find what quadrilateral the shape of the pool will
represent. The Flannery family is putting an in-ground pool in their backyard. Knowing
that they’re putting the pool in their backyard is not going to help us to know the shape of
the pool, so we will eliminate this fact. The pool company told them that they could use
any shape quadrilateral they wanted for the pool. This fact does not help us to find what
quadrilateral the shape of the pool will be. So we will eliminate this fact as well. Mrs.
Flannery told her daughter, Chloe, that the pool was going to have two right angles.
Knowing that the pool will have two right angles will help us to find out what type of
quadrilateral the shape of the pool represents. So we will keep this fact. And one pair of
parallel sides, knowing that the pool has one pair of parallel sides is also important to
finding out the shape of the pool. Now that we have eliminated the unnecessary facts, we
will list the necessary facts. The pool is a quadrilateral, it has two right angles, it has one
set of parallel sides.
In Step L, we will Line Up a Plan. First we need to choose an operation or operations to
help us to solve the problem. In this problem we will not have an operation as we are
looking to classify the shape of the pool. We will write the word none for our operation.
Now let’s write in words what your plan of action will be. We can look at the chart of
quadrilaterals to see what quadrilateral has the listed attributes.
We are now ready to Verify Your Plan with Action. First we estimate your answer.
Since we are using the chart of quadrilaterals to see which quadrilateral has the listed
attributes will not have an estimate for our answer. We will move right into carrying out
your plan. The attributes on Step O were that the pool has two right angles and it has one
set of parallel sides. Looking at the chart of quadrilaterals the only quadrilateral that has
the attributes of one set of parallel sides is a trapezoid. A trapezoid has one set of parallel
sides. So the pool will be in the shape of a trapezoid.
In Step E, we will Examine Your Results. Does your answer make sense? Here compare
your answer to the question. Yes, because I am looking for the shape of the pool. Is your
answer reasonable? Here compare your answer to the estimate. Since we did not have an
estimate for this problem, this question is not applicable. And is your answer accurate?
Here you want to check your work. Yes our answer is accurate. We are now ready to
write your answer in a complete sentence. The pool will be in the shape of a trapezoid.
Now let’s go back and discuss the essential questions from this lesson.
Our first question was, explain the difference between a rectangle and a square. The
rectangle has two separate pairs of congruent sides, and a square has all four sides
congruent.
Our second question was, how do you know if a quadrilateral is a parallelogram? A
quadrilateral is a parallelogram if it has two pairs of congruent parallel sides.
And our third question was, sketch an example of a quadrilateral that is not a rectangle,
square, parallelogram, rhombus or trapezoid. Answers will vary, but none of the answers
should have parallel sides.
Here are some examples: