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45-45-90 Special Right Triangle Assignment Abroad


The answer can be found two different ways. The first step is to realize that this is really a triangle question, even though it starts with a square. By drawing the square out and adding the diagonal, you can see that you form two right triangles. Furthermore, the diagonal bisects two ninety-degree angles, thereby making the resulting triangles a  triangle. 

From here you can go one of two ways: using the Pythagorean Theorem to find the diagonal, or recognizing the triangle as a  triangle.

1) Using the Pythagorean Theorem

Once you recognize the right triangle in this question, you can begin to use the Pythagorean Theorem. Remember the formula: , where  and  are the lengths of the legs of the triangle, and  is the length of the triangle's hypotenuse.

In this case, . We can substitute these values into the equation and then solve for , the hypotenuse of the triangle and the diagonal of the square:

The length of the diagonal is .

2) Using Properties of  Triangles

The second approach relies on recognizing a  triangle. Although one could solve this rather easily with Pythagorean Theorem, the following method could be faster.

 triangles have side length ratios of , where  represents the side lengths of the triangle's legs and  represents the length of the hypotenuse.

In this case,  because it is the side length of our square and the triangles formed by the square's diagonal.

Therefore, using the  triangle ratios, we have  for the hypotenuse of our triangle, which is also the diagonal of our square.

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.

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.
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Teaching Duration

45 minutes