Chapter 11 Lesson 1
Working with Shapes
Name 3 parts that
decide each triangle.
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What's your favorite shape?
Squares. 4 equal sides,
no worries, no measuring.
Sorry, too many sides.
What shape has less sides?
4 sides is too many?
It can't have just 2 sides
so, it has to have 3 sides.
Triangles
This lesson is all about triangles.
Ok, they have 3 sides.
Now, moving onto squares.
It's alittle more complicated than that.
One kind has
Equal Angles and Equal Sides
1. Equal Angles
2. Equal Sides
Equal angles? Equal sides?
What triangle does that?
Equilateral
Triangle
There you are.
It does what a square does.
3 Equal Sides
3 Equal 60 Angles
How did you know all
the angles are 60 degrees?
Every triangle in the universe
has the same number of degrees.
Triangle:
180 degrees
The angles add upto 180.
Really? Every triangle
in the universe adds to 180?
That's pretty amazing.
For sure. Here's
another triangle fact.
What do you call a triangle
that has a right angle?
Right Triangle
It's got to be a right triangle.
Right. One angle is 90 degrees.
What if 2 angles are the same?
Isoceles Triangle
That's a weird name.
Isoceles Triangle
2 Equal Sides means
2 Equal Angles.
Here's how to remember it.
Oh, yeah. What else is there?
What would
you call this triangle?
I'd call it really big.
How am I supposed to know?
Obtuse
Angle
What's an obtuse angle?
Obtuse
Angle
The angle is over 90 degrees.
Don't tell me. Make a triangle.
Obtuse
Triangle
That's why we don't let
you name the triangles.
Obtuse triangle has 1 obtuse angle.
Try another. What would
you call this triangle?
I'd call it the mountain.
I could ski down that.
I'd visit you in the hospital.
We call this one an
Acute
Triangle
I should have got that one.
All the angles are acute.
You could ski down this one.
You'd fall down the other one.
I call that a bunny hill.
Ok, what's the name this time?
It's called a
Scalene Triangle.
All the angles are different
and all the sides are different.
It's also an obtuse angle.
Too many kinds of triangles.
That's why I like squares.
Oooh, hate to ruin it, but there's
lots of 4 sided shapes, too.
I guess you know what's next.
Qs
How many degrees does
each triangle's angles add to?
180
All triangles add upto 180 degrees.
What's a right triangle?
Right Triangles
have a 90 degree angle.
A square shows the angle.
What's an acute and obtuse triangle?
Acute Triangle:
All less than 90.
Obtuse has 1 angle
more than 90.
Equilateral
Isoceles
How are equilateral and
isoceles triangle different?
Equilateral
Isoceles
Equilateral has 3 sides equal.
Isoceles has 2 sides equal.
How many sides are equal
in a scalene triangle?
Scalene Triangle
No sides are equal.
Chapter 11 Lesson 1a
Working with Shapes
Name 4 types of quadrilaterals.
Finally. Can
we do some squares?
Sure, but now we'll
call them quadrilaterals.
What makes a quadrilateral?
I know, I know. It has 4 sides.
Triangle angles add to 180.
How many degrees are in
all 4 quadrilateral angles?
Quadrilaterals
360 degrees
360? That seems like alot.
Think about 4 right angles.
Each one is 90 degrees.
Add them is 360 degrees.
Here's some of the features.
1. Equal Angles
2. Equal Sides
3. Right Angles
Same stuff as triangles.
1. Equal Angles
2. Equal Sides
3. Right Angles
True, but we'll add 1 more.
4. Parallel Lines
I know. Squares have those, too.
Lots of quadrilaterals do.
Ok, we'll start off with square.
Square
What do you want?
They're square.
You know parallel lines. Tell
me 2 other things about them.
1. 4 Equal Sides
2. 4 Right Angles
Oh, those kinds of things.
Why do you
like squares so much?
What do pizzas come in?
I should have known.
What if 2 sides get longer?
Rectangle
It's called a rectangle.
Rectangle
Name 3 things about rectangle.
1. 4 Right Angles
2. Parallel Sides
How do I say it's
longer than it is wide?
2 Sets Of
Equal Sides
Now it's 2 sets of equal sides
instead of 4 equal sides.
Works for me. Are there
any other quadrilaterals?
Square
What if we take
a square and bend it?
Rhombus
It doesn't look like a square.
Rhombus
It still has 4 equal sides.
How is it different from square?
Rhombus
It doesn't have 4 right angles.
Rhombus
So, tell me about the angles.
b
a
Rhombus
b
a
Opposite angles are the same.
b
a
b
a
Tell me about parallel lines.
a
b
b
a
Opposite sides are parallel.
a
b
b
a
Altogether, tell me 3 things
that make a rhombus.
1. 4 Equal Sides
2. Opposite angles equal
3. Opposite sides parallel
I'll just remember the picture.
Time for a different quadrilateral.
What if we do the same
thing to a rectangle?
Parallelogram
It's a rectangle
without 4 right angles.
Parallelogram
Same rules as Rhombus.
Look at the rules again.
1. 2 sets equal sides
2. Opposite angles equal
3. Opposite sides parallel
What does a
parallelogram look like?
Parallelogram
Rectangle without right angles.
I'll take a parallelogram
and make a new figure.
Take a parallelogram and
move the angle outwards.
Watch the new shape.
Trapezoid
Oooh, it looks like
the opening to Star Wars.
Trapezoid
It does look alittle 3D.
Do you see 2 right triangles
and a rectangle inside it?
Trapezoid
I see Luke and Darth Vader.
"Luke, Luke, I am your father."
...................
...................
Trapezoid
Oh, yeah. There's a
rectangle with 2 right triangles.
It looks like they're bookends.
But, they aren't always equal.
...................
...................
Trapezoid
Which of these are trapezoids?
I don't think any of them are.
They are all trapezoids.
What makes a trapezoid?
parallel
Trapezoid
parallel
2 sides are parallel.
That's the only thing it needs.
parallel
Trapezoid
parallel
2 sides are parallel.
Yeah, lots of quadrilaterals.
Triangles
Quadrilaterals
It is alot but just think about
equal sides and right angles.
Square is still my favorite.
I kind of know what you mean.
Qs
How many degrees are
in any quadrilateral?
360 degrees
4 x 90 is 360 degrees.
How is a rhombus
different from a square?
Rhombus
b
a
b
a
Square with no right angles.
How is a parallelogram
different from a rectangle?
Parallelogram
b
a
b
a
Rectangle
with no right angles.
Trapezoid
How is a trapezoid different
from a parallelogram?
Trapezoid
One side is moved out.
2 sides have to be parallel.
Chapter 11 Lesson 1
Working with Shapes
Short Lesson
Triangles and Quadrilaterals.
Triangles
There are 3 things
we'll study about triangles.
1. Equal Angles
2. Equal Sides
3. Right Angles
We'll start with equal sides.
Here's the easiest triangle.
Equilateral
Triangle
It has 3 equal sides.
You know it also has...
3 Equal 60 Angles
Important Fact:
180 degrees
All triangles have 180 degrees.
What do you call a triangle
that has a right angle?
Right Triangle
Right triangles have
1 angle that's 90 degrees.
Here's another with equal sides.
equ
al s
ide
ide
al s
equ
eq
e
d
ua
i
s
l
l si
a
u
de
eq
Isoceles Triangle
They have 2 Equal Sides.
How many equal angles?
equ
al s
ide
ide
al s
equ
eq
e
d
ua
i
s
l
l si
a
u
de
eq
Isoceles Triangle
2 Equal Angles.
There is a different
kind of triangle.
Obtuse
Triangle
It's called an obtuse triangle.
The angle is over 90 degrees.
There is another one like it.
Acute
Triangle
All the angles are acute.
Each is less than 90 degrees.
There is 1 more angle we use.
Scalene
Triangle
Scalene triangles have
3 different sides and angles.
Next, what shapes have 4 sides?
Quadrilaterals
have 4 sides.
Each quadrilateral has the
same number of degrees.
360 degrees
What does a square have
that a triangle can't do?
Parallel Lines
Squares have parallel lines.
Make 2 sides longer.
What shape is it?
Rectangle
It's longer
than it is wide.
We'll go back to the square.
Square
What if we take
a square and bend it?
Watch what happens.
Rhombus
It doesn't have 4 right angles.
Which angles are the same?
b
a
Rhombus
b
a
Opposite angles are the same.
Try the same
thing with a rectangle.
What if we do the same
thing to a rectangle?
Parallelogram
It's a rectangle
without 4 right angles.
Same rules as Rhombus.
Take a parallelogram and
move the angle outwards.
What does it look like?
Trapezoid
Do you see 2 right triangles
and a rectangle inside it?
It has a rectangle
with 2 right triangles.
We'll make some shapes.
...................
...................
Trapezoid
Which of these are trapezoids?
They are all trapezoids.
What makes a trapezoid?
parallel
Trapezoid
parallel
2 sides are parallel.
We'll call the others
imperfect trapezoids.
Questions
How many degrees does
a triangle's angles add to?
Triangle:
180 degrees
What's the name for a
triangle with 3 equal angles?
Equilateral
Triangle
3 Equal 60 Angles
means
3 Equal Sides
What makes a right triangle?
Right Triangle
It has a right angle.
What makes an
acute and obtuse triangle?
Obtuse: One
angle is over 90.
Acute: all angles
are smaller than 90.
How many degrees are
in any quadrilateral?
Quadrilaterals
360 degrees
What sides and angles
make it a square?
Square
4 Equal Sides
4 right angles
How is a rhombus
different from a square?
b
a
Rhombus
b
a
No right angles.
Opposite angles are equal.
What shape
is longer than a square?
Rectangle
2 sides are longer.
How is a parallelogram
different from a rectangle?
Parallelogram
b
a
b
a
It's a rectangle with
no right angles.
Opposite angles are equal.
How does a parallelogram
change to make a trapezoid?
Trapezoid
Move 1 side out.
Trapezoid has 2 parallel sides.
Chapter 11 Lesson 1
Working with Shapes
Practice #1
Triangles and Quadrilaterals.
How many degrees does
each triangle's angles add to?
180
All triangles add upto 180 degrees.
What's a right triangle?
Right Triangles
have a 90 degree angle.
A square shows the angle.
What's an acute and obtuse triangle?
Acute Triangle:
All less than 90.
Obtuse has 1 angle
more than 90.
Equilateral
Isoceles
How are equilateral and
isoceles triangle different?
Equilateral
Isoceles
Equilateral has 3 sides equal.
Isoceles has 2 sides equal.
How many sides are equal
in a scalene triangle?
Scalene Triangle
No sides are equal.
Problems
Isoceles
What does an isoceles
triangle look like?
Isoceles Triangle
2 sides are equal
Scalene
What does a scalene
triangle look like?
Scalene
Triangle
All the angles and sides
are different.
Equilateral
What does an equilateral
triangle look like?
Equilateral
Triangle
3 Equal Sides
Same thing as a square,
but with 3 sides.
Acute Triangle
What makes an acute triangle?
Acute
Triangle
All the angles are less than 90.
Obtuse Triangle
What makes an obtuse triangle?
Obtuse
Triangle
One of the angles is more than 90.
Right Triangle
What's a right triangle?
Right Triangle
Have a 90 degree angle.
A square shows the angle.
Chapter 11 Lesson 1
Working with Shapes
Practice #2
Different questions.
Triangles and Quadrilaterals.
How many degrees are
in any quadrilateral?
Quadrilaterals have
360 degrees
4 x 90 = 360
How is a rhombus
different from a square?
Rhombus
b
a
b
a
Square with no right angles.
How is a parallelogram
different from a rectangle?
Parallelogram
b
a
b
a
It's a rectangle
with no right angles.
Trapezoid
How is a trapezoid different
from a parallelogram?
Trapezoid
One side is moved out.
2 sides have to be parallel.
Problems
What shape has 4 90 degree
angles and equal parallel sides?
Square
How is a rectangle
different from a square?
Rectangle
A rectangle has 2 sides
that are longer.
Rhombus
How is a rhombus
different from a square?
b
a
Rhombus
b
a
It doesn't have right angles.
The opposite angles are the same.
b
a
Rhombus
b
a
How is a parallelogram
different from a rhombus?
Parallelogram
b
a
b
a
Parallelograms are longer,
just like rectangles are.
b
a
Parallelogram
b
a
How is a trapezoid different
from a parallelogram?
Trapezoid
It's a quadrilateral with
one side moved out.
Only 2 sides are parallel.
Name 2 shapes with equal
sides and equal angles.
Equilateral
Triangle
3 Equal 60 Angles
Square
4 Equal 90 Angles
Chapter 11 Lesson 1
Working with Shapes
Performance #1
Triangles and Quadrilaterals.
What shape has...
1. opposite parallel sides
2. all sides are equal
3. 4 right angles
Square
4 right angles
4 equal sides
Parallel sides
What shape has...
1. opposite parallel sides
2. 2 sides are longer
3. no right angles
Parallelogram
b
a
b
a
Parallelograms are longer,
just like rectangles are.
What shape has...
1. 3 equal sides
2. equal angles
Equilateral
Triangle
Equal sides,
Equal angles.
a
50
If a right angle has a 40 degree
angle, what is angle a?
a
50
If a right angle has a 40 degree
angle, what is angle a?
55 + 55 + ?
What kind of triangle is it?
What's the 3rd angle?
Isoceles
Triangle
55 + 55 + ?
110 + 70
The 3rd angle is 70 degrees.
a
50
If a quadrilateral has a 50 degree
angle, what is angle a?
130
50
6)
130 + 50 = 180
130 + 50 degrees is 180.
Chapter 11 Lesson 1
Working with Shapes
Performance #2
Triangles and Quadrilaterals.
What shape has...
1. 2 equal length sides
2. 2 equal angles
Isoceles Triangle
Equilateral Triangles have
2 equal sides and angles.
What shape has...
1. opposite parallel sides
2. 2 sides are longer
3. right angles
Rectangle
A rectangle has 2 sides
that are longer.
What shape has...
1. 3 equal sides
2. equal angles
Equilateral
Triangle
Equal sides,
Equal angles.
What shape has...
1. 3 sides
2. a right angle
Right Triangle
Every right triangle
has a right angle.
?
25
90
If a right angle has a 25 degree
angle, what's the 3rd angle?
75
25
90
115 + 75
The 3rd angle is 75 degrees.
a
40
If a rhombus has a 40
degree angle, what is angle a?
140
40
140 + 40 = 180
140 + 40 degrees is 180.