45-45-90 Special Right Triangle Assignment Of Rents

Product Description

Right Triangles - 45 45 90 Special Right Triangles Notes and Practice

This packet includes information on teaching 45 45 90 Special Right Triangles. I have included:

*** Teacher Notes with worked out formulas, diagrams and workout examples. (the diagram on the first page comes from my set of Right Triangle Unit Vocabulary Cards and Posters)

*** Student Notes so that they can follow along and work out the problems as the teacher explains the information

*** A 22 question practice/homework sheet that includes an answer key.
*****************************************************************************
I also have a similar set of notes available on
30-60-90 Special Right Triangles
30 60 90 Special Right Triangles Notes and Practice.

You can also buy my
45-45-90 and 30-60-90 Right Triangle Notes bundled together at:
Special Right Triangles 45-45-90 and 30-60-90 Notes and Practice Bundle.

Please check out my other right triangle resources:

Right Triangles Trig Bellwork/Exit Cards/Station Questions
Geometry Right Triangles Trig Bellwork Exit Cards Station Questions.

Vocabulary and Games
Geometry Right Triangles Trigonometry Square Roots BINGO Game.
Geometry Right Triangles Trigonometry Square Roots Vocabulary Matching Activity.

Classroom Notes with Assignments and Answer Keys:
Soh Cah Toa (Sin Cos Tan) Introduction To Trigonometry Notes and Practice.
The Pythagorean Theorem Notes and Practice.
The Law of Sines Notes and Practice.
Angles of Elevation and Depression Notes and Practices One and Two.
Square Roots and Simplifying Radicals.

Converse of the Pythagorean Theorem Investigation Activity:
The Converse of The Pythagorean Theorem Investigation Activity.

Wall Posters for Display of Main Concepts:
Right Triangle Unit Vocabulary Cards and Posters.
Right Triangle Unit Vocabulary CCSS and I-Cans Wall Hangings.

Vocabulary Assignment and Puzzles
Right Triangle Unit Vocabulary Assignment and Puzzles.

Extra Practice Worksheets
Sin Cos and Tan Soh Cah Toa Trigonometry Riddle Practice Worksheet.
Geometry Pythagorean Theorem Riddle Worksheet.
Geometry Simplifying Square Roots Riddle Worksheet.
Geometry Special Right Triangles Practice Riddle Worksheet.
Geometry Angles of Elevation and Depression Riddle Practice Worksheet.

Graphic Organizers:
Right Triangles and Trigonometry Graphic Organizers.

Unit Review:
Right Triangles Unit Review.

Notecards
Geometry Right Triangles Trigonometry Square Roots Note Cards.

While each product can be purchased individually at the above links -- You can save 20% by buying the entire unit bundled together!!!

Right Triangles Complete Unit Bundle
Geometry Right Triangles Complete Unit Bundle.
*****************************************************************************
Customer Tips:

How to get TPT credit to use on future purchases:
• Please go to your My Purchases page (you may need to login). Beside each purchase you'll see a Provide Feedback button. Simply click it and you will be taken to a page where you can give a quick rating and leave a short comment for the product. Each time you give feedback, TPT gives you feedback credits that you use to lower the cost of your future purchases. I value your feedback greatly as it helps me determine which products are most valuable for your classroom so I can create more for you. ☺

Be the first to know about my new discounts, freebies and product launches:
• Look for the green star next to my store logo and click it to become a follower. Voila! You will now receive email updates about this store. ☺

*****************************************************************************


Report this Resource

Teaching Duration

45 minutes

Something special in geometry
is the 45, 45, 90 triangle.


Well, a 45, 45, 90 triangle is an isosceles
right triangle where these two legs
are congruent to each other.
The reason why it's 45, 45, 90 is because
if we know that these two angles are
congruent to each other, because the
isosceles triangle theorem, then
we can say that 180 degrees is equal
to 90, plus X plus X. So if
I add these up, I'm going to have 180
is equal to 90, plus 2 X, so I'm
going to subtract 90 from both sides
and I get 90 is equal to 2X, and
then I'm going to divide by 2 to
solve for X. And 90 divided by
2 is 45, which means each of these angles
that are congruent to each other
have to be 45 degrees.


So in an isosceles right triangle you're
going to have a 45 degree, a 45 degree
and a 90 degree.
So that's we mean when
we say 45, 45, 90.


Now something is going on with
these angles and sides.
And if I wrote in that these were both X and
I would say that this is my hypotenuse
C, let's apply the Pythagorean
theorem and see what happens.


Pythagorean theorem says A squared plus
B squared equals C squared and A and
B here are both X. So I'm going to
write that X squared plus X squared
is equal to C squared.
I can combine like terms here and X squared
plus X squared is 2X squared.
So if I want to solve for my hypotenuse
C, I'm going to take the square root
of both sides, and the square root
of X squared is X, and there is no
whole number square root of 2. So
C is equal to X times the square
root of 2. Well, that's a little
difficult to understand.


So let's say we had an isosceles right triangle
with sides of length 1 and I'm
trying to find the hypotenuse.
So maybe this will make sense
with this triangle.


Here we'll have 1 squared plus 1
squared is equal to C squared
Well, 1 plus 1 is 2. So if I take the
square root of both sides, I find
that my hypotenuse is equal to the
square root of 2. So now what
I see it's talking about is if you know
the side of one of your legs, if
you know that length, you're going to.
multiply it by the square root of 2.
So to get from the leg in a 45, 45, 90.
triangle, you're going to multiply by
the square root of 2.


Let's say, however, you don't know what that
leg is. And you know the hypotenuse.
So I'm going to draw another
triangle over here.
45, 45, 90, and let's say you said this
was 3. To go from your hypotenuse
to your leg, you're going to undo multiplying
by the square root of 2.
So you're going to divide by the square
root of 2. So this answer
right here will be 3 divided by the
square root of 2.


And we can't
have a square root in our denominator here.
So now this is becoming quite a chore.
We're going to multiply by square root
of 2. Multiply by the square root
of 2. So we'll have in our numerator
3 times the square root of
2. Square root of 2 times square root of 2
is 2 because you'll have the square root
of 4. So this is actually 3 times.
the square root of 2 divided by 2.


So if we go back to our original
drawing here where we said.
for any right triangle where you have
two legs that are congruent, to go
from your leg to your hypotenuse, all
you need to do is take that number
and multiply it by the square root of
2. So if X is 5, your hypotenuse
is 5 times the square
root of 2. To go from your hypotenuse back to one of
your legs, you're going to divide by
the square root of 2.


So keep that in mind and solving for missing
sides, an isosceles right triangle
is pretty simple.

Comments

Leave a Reply

Your email address will not be published. Required fields are marked *