The Special Right Triangle Show Featuring The 45°-45°-90° Triangle And The 30°-60°-90° Triangle.

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Presentation transcript:

The Special Right Triangle Show Featuring The 45°-45°-90° Triangle And The 30°-60°-90° Triangle

Act 1 – Scene 1 Andy 45°-45°-90°

Setting Andy 45°-45°-90° Triangle enters the stage and stares into the mirror. As he looks at the image looking back at him he notices something he has never noticed before.

The Look Wow, I have never noticed that the sides of my face are the SAME LENGTH!!

Making Connections It’s kind of like they have a relationship and I can call them both x. X X

Closer Look Andy 45°-45°-90° stared closely into the mirror and noticed something else. He could not believe his eyes. He thought to himself this must be the same for all of my 45°-45°- 90° brothers and sisters, cousins, all of the 45°-45°-90° family!

*Bright Idea* XX 45° Both the X’s are opposite my 45° angles.

*Even Brighter Idea* XX 45° The length of the bottom of my face is

The Moment of Truth Andy 45°-45°-90° started to think to himself and realized that in all 45°-45°-90° triangles, whatever value is chosen for x, it remains the same for all the x’s. All 3 sides of his face had a relationship with each other! When he knew the length of one, he could find the missing sides!

A Second Glance XX 45° I measured the side of my face and it is 6 inches! That must mean both sides of my face are 6 inches. 6 6 That also must mean that the bottom of my face is ….

The Family Reunion The 45°-45°-90°’s always planned a family reunion about this time of year. Nice time to get together and celebrate the holidays. Andy 45°-45°-90° was ready to wow his cousins with his new found information. He was going to ask his cousin for the length of one side of his face and tell him he could find the other two sides!

Presenting Andy 45°-45°-90° The Great! Jordan, bettcha if you give me the length of one side of your face, I can tell you the other two! NO WAY! Prove it! The length of the left side of my face is 3. 3

The Challenge Ha so easy! The right side of your face is 3 also and the bottom of your face isWOW Andy, your amazing!

A Closer Look 45° X X All three X’s are the SAME VALUE!

Example A Given a 45°-45°-90° triangle, with the measure of AB = 12. What are the other two sides? 45° 12 C A B 12 AC = BC =

Example B Given a 45°-45°-90° triangle, with the measure of BC = 16. What are the other two sides? 16 C A B AB = BC =

How’d We Do That?! 16 C A B We know that 16 must be = LET’S SOLVE FOR X! Set equal to each other Divided both sides by radical 2, to get x alone. Multiply left side by radical 2 over radical 2.

How’d We Do That Cont. Radical 2 times radical 2 simply leaves us with 2. Reduce 16 over 2 to 8. RULE When given the hypotenuse of a °-45°-90° triangle, simply divide it by 2 and multiply it by radical 2 for the length of the other two sides.

IntermissionTake this time to work on a few examples of 45°-45°-90° triangles! Remember the rules and what you know about the lengths of the sides. 45° X X

Act 1 – Scene 2 Meeting His Match

A Show On The Road Andy then took his show on the road traveling from city to city showing that he could determine the missing lengths of the sides of a 45°-45°-90° when given just a single side.

The Show My hypotenuse is equal to 14 what are my sides?! Seth, that’s a joke right? SO EASY, both of your sides are 7√2 Gosh! You got it!

The Show One of my sides equals 6. What is the other one and the hypotenuse? David, that one is even easier than the one before! The other side is 6 and your hypotenuse is 6√2 How’d you do that!!!

I think I can stump you Andy, my side equals 5√2. Nice try Kayla! But I have figured you out as well, your other side is 5√2. And, Miss your hypotenuse is 10! WOW he is amazing!

You’ll never figure me out! One of my sides equals 12√3! Once again, Jada, I have figured you out as well, your other side is 12√3. your hypotenuse is 12√6! Simply Amazing, Ms. Balboni must have taught him!

This is certainly the one to stump you! One of my sides equals 5√8! If you thought you got me, you haven’t, your other side is 5√8. And, Thomas your hypotenuse is 20! I give up, he really knows his stuff!

How about me Andy! On of my sides is 5!! Andy look and he stared. He had never seen anything quite like Robin. He knew she wasn’t a 45°- 45°-90° but he did know there was something special about her! Come on Andy. Don’t tell me I stumped you!