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Unit 7!
Special Right Triangles!
WARM UP - Radical Review Problems!
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Simplify:!
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5. 2 3 • 4 7 !
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OVER —->!
The AA Similarity Theorem!
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For any two triangles, if two pairs of corresponding angles are equal, then the triangles are similar.!
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∆ABC ~ ∆PQR!
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12.
GIVEN: ∆RST with # GH || RS ! !
PROVE: ∆RST~∆HGT!
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GROUP 1 - Pythagorean Triples!
THE 3 - 4 - 5 TRIANGLE FAMILY!
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A Pythagorean Triple is a set of three counting numbers that are the lengths of the sides of
a right triangle.!
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15
10
5
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6
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12
The triangles above are all members of the (3, 4, 5) family. !
For example, the triple (6, 8, 10) is ( 3• 2, 4 • 2, 5 • 2) .!
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Problems:
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(3, 4, 5)!
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A.!
20
Find the missing side in each triangle:!
Solve for x. ! !
x
15
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DO YOU NOTICE A PATTERN?!
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B.!
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C.!
45
x
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In triangle A, the leg that is 15 units long is __ i 5 , the leg that is 20 units long is __ i 5 ,
and x = ____, which is __ i 5 .!
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In these problems, use what you learned about the 3-4-5 family to predict what x will be.!
Check by using the
pythagorean theorem to
solve.
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3. Come up with 2 more right triangles in the 3-4-5 family. !
GROUP 2 - Pythagorean Triples!
THE 5 - 12 - 13 TRIANGLE FAMILY!
A Pythagorean Triple is a set of three counting numbers that are the lengths of the sides of
a right triangle.!
13
26
10
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For example, the triple (10, 24, 26) is (5 • 2,
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The triangles above are all members of the (5, 12, 13) family. !
(5, 12, 13)!
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A.!
Solve for x.! !
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12 • 2, 13• 2) .!
B.!
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C.!
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DO YOU NOTICE A PATTERN?!
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1. In triangle A, the leg that is 26 units long is __ i 2 , the leg that is 24 units long is __ i 2
and x = ____, which is __ i 2 .!
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2. Use what you learned about the 5-12-13 family to find what x will be.!
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Check by using the
pythagorean theorem to
solve.
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3. Come up with 2 more right triangles in the 5-12-13 family. !
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GROUP 3 - Pythagorean Triples!
THE 7 - 24 - 25 TRIANGLE FAMILY!
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Use what you know about the 7-24-25 family to find what x will be.!
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GROUP 4 - Pythagorean Triples!
THE 8 - 15 - 17 TRIANGLE FAMILY!
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Use what you know about the 8-15-17 family to find what x will be.!
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Geometry!
Special Right Triangles!
Unit 7 HOMEWORK #1!
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1. For each triangle below, identify what family it is and then find x without solving! YOu
can check by using the Pythagorean Theorem to solve.!
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A.!
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B.!
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C. !
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x
family: ________!!
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family: ________!!
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family: ________!!
x = _______!
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x = _______!
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x = _______!
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2. Solve for x by using the Pythagorean Theorem.!
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3. Find QD using what you know about Pythagorean Triple families.!
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Given: || !
Prove; ∆PQR ~ ∆TSR
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Statements! !
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Reasons!
3. Tell which family is represented by each each triangle, by what factor, and then give the
missing side. If the triangle does not belong to a family then use the pythagorean theorem.!
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