45-45-90 Special Right Triangle Assignment Of Mortgage

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.

Product Description

Right Triangles (Special)- 45 45 90 Riddle Practice Worksheet

This riddle practice worksheet covers 45 -45 - 90 Special Right Triangles by asking students to solve for either the missing leg or for the hypotenuse. When they find their answer, they look in the solution box to find the corresponding color to complete the Riddle!

The worksheet includes 15 problems, 9 which include a diagram and 6 story problems.

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If you are in need of other right triangle resources please check out:

Task Cards
The Pythagorean Theorem and It's Converse.
Trigonometry (Sine-Cosine-Tangent).
Special Right Triangles.

Quizzes:
Special Right Triangles Quiz.
Pythagorean Theorem, Converse and Triples Quiz.
Trigonometry and Angles of Elevation and Depression Quiz.

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

Quick Reference Sheet
Geometry Right Triangles and Trigonometry Quick Reference Sheets.

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

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

Extra Practice Worksheets
Geometry Special Right Triangles 30 - 60 - 90 Riddle Practice Worksheet.
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.

I also have Seven Sets of Notes:

Part One:
Square Roots and Simplifying Radicals.

Part Two:
The Pythagorean Theorem Notes and Practice.

Part Three
30 60 90 Special Right Triangles Notes and Practice.

Part Four
45 45 90 Special Right Triangles Notes and Practice.

Part Five
Soh Cah Toa (Sin Cos Tan) Introduction To Trigonometry Notes and Practice.

Part Six
Angles of Elevation and Depression Notes and Practices One and Two.

Part Seven
The Law of Sines Notes and Practice.

Or you can purchase the whole unit (notes and resources) at:
Geometry Right Triangles Complete Unit Bundle.
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