Geometry 8.4 Special Right Triangles This is a very important section, as it is used extensively throughout the second semester.

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Presentation transcript:

Geometry 8.4 Special Right Triangles This is a very important section, as it is used extensively throughout the second semester.

All you need to know is how to multiply by root two and divide by root two.

Triangles 45 o o x x Since all triangles are similar, by AA Similarity Postulate, this formula works for all triangles. The formula.

Does it work for the Pythagorean Theorem? 45 o o x x ? 2x = 2x ? Yes! 22

The Two Types of Problems 45 o o 3 3 Type 1: Given the length of a leg, solve for the other leg and hypotenuse. o o What are the other two lengths? What are the other two lengths? Multiply by root 2.

The Two Types of Problems 45 o o 7 Type 2: Given the length of the hypotenuse, solve for the two legs. o o What are the other two lengths? What are the other two lengths? Shortcut: Divide the length of the hypotenuse by 2 and multiply by to find the length of the leg. Divide by root 2.

I Solve leg ABBCAC A leg B C 45 

Let’s Try Some From the HW P. 302 #18, 26 P. 288 #28

HW P. 302 (1-8, 17, 18, 23, 26, 27) P. 288 #27-30 Quiz on Thursday Please sign up for School Loops(there is a link on my webpage) Answers to the packet below if you want to work them out:

Geometry 8.4 Special Right Triangles Part 2 This is a very important section, as it is used extensively throughout the second semester.

All you need to know is how to multiply and divide by two and multiply and divide by root three.

Triangles 60 o 30 o x 2x Since all triangles are similar, by AA Similarity Postulate, this formula works for all triangles. The formula.

Does it work for the Pythagorean Theorem? 60 o 30 o 2x x ? x + 3x = 4x ? Yes! 222

The Three Types of Problems 30 o 60 o 5 10 Type 1: Given the length of the short leg, solve for the long leg and hypotenuse. o 30 o What are the other two lengths? What are the other two lengths? Multiply by root 3. Multiply by 2. Multiply by root 3. Multiply by 2.

The Three Types of Problems 60 o 30 o 9 Type 2: Given the length of the hypotenuse, solve for the two legs. o 60 o What are the other two lengths? What are the other two lengths? Multiply by root 3. Divide by 2. Multiply by root 3.

The Three Types of Problems 30 o 60 o 9 Type 3: Given the length of the long leg, solve for the short leg and hypotenuse. o 30 o What are the other two lengths? What are the other two lengths? Shortcut: Divide the length of the long leg by 3 and multiply by to find the length of the short leg. Multiply by 2. Divide by root 3. Multiply by 2 Divide by root 3.

B A 2(leg) leg C 60  30  II Solve: leg ABBCAC

x x x x x 60 9 x III. Solve for x

Let’s Try A Few From the HW P. 302 #20, #22 P. 288 #31

HW P. 302 (9-16) P. 302 (19-25, skip 23) P. 288 (31,32) Quiz Friday Here are the answers to your packet if you want to work them out.