why does the line y = x only have one slope? what is true about all of the triangles? how does this...
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Answers to Homework 1) Yes, > 20 2) No, < 13 3) Yes, 2 + √7 > 4 4) = = = 400 Right Triangle 5) (6 √3 ) 2 + (8 √3 ) 2 = (10 √3 ) < < 300 Right Triangle 6) ( √12 ) 2 + ( √21 ) 2 = (4 √2 ) > 32 33> 32 Acute Triangle 7) = > 100 Acute Triangle 8) (4 √2 ) 2 + (4 √2 ) 2 = (8) = 64 Right Triangle 9) = < Obtuse Triangle 10) = > 6400 Acute TriangleTRANSCRIPT
Why does the line y = x only have one slope?
What is true about all of the triangles?
How does this relate to Pythagorean Theorem?
Right TrianglesDay 3 – Special Right Triangles
Answers to Homework1) Yes, 12 + 15 > 202) No, 5 + 6 < 13
3) Yes, 2 + √7 > 4
4) 122 + 162 = 202 144 + 256 = 400 400 = 400 Right Triangle
5) (6√3)2 + (8√3)2 = (10√3)2 108 + 192 < 300 300 < 300 Right Triangle
6) (√12)2 + (√21)2 = (4√2)2 12 + 21 > 32 33> 32 Acute Triangle
7) 82 + 72 = 102 64 + 49 > 100 Acute Triangle
8) (4√2)2 + (4√2)2 = (8)2 32 + 32 = 64 Right Triangle
9) 282 + 962 = 1102 784 + 9216 < 12100 Obtuse Triangle
10) 592 + 602 = 802 3481 + 3600 > 6400 Acute Triangle
Answers to Homework11) 122 + (12√3)2 = 242
144 + 432 = 576 Right Triangle
12)52 + (√60)2 = 82 25 + 60 > 64 Acute Triangle
13)PR2 + RQ2 = PQ2
(√10)2 + (√20)2 = (√26)2 10 + 20 > 26 Acute Triangle
14)(a)2 + (b)2 = (c)2 (2n)2 + (n2 - 1)2 = (n2 + 1)2 4n2 + n4 - 2n2 + 1 = n4 + 2n2 + 1 2n2 + 1 = 2n2 + 1 Yes, this method will work because both sides of the equation are equal.
15)
Statements Reasons1. AB = 4, BC = 2, AC = √10 1. Given2. AB2 + AC2 = BC2 2. Pythagorean Theorem 3. 22 + (√10)2 = 42 3. Substitution 4. 14 < 16 4. Substitution
5. ABC is an obtuse triangle 5. Pythagorean Theorem Converse
6. ABC is acute angle 6. Definition of obtuse triangle
7. 1 is an acute angle 7. Vertical Angles are Congruent
Objective To find the side length of special right triangles
Homework Special Right Triangles Worksheet
Need help? Look in your book – Section 9.4
Special Right Triangles Find the length of the hypotenuse
8
8
22 28 8x
x
2 642x 2 128x 8 211.31
xx
1
1x
22 21 1x
2 2 1x 2 2x 2
1.41xx
s
sx
22 2x s s
22 2x s22 2x s2x s
Isosceles Right Triangles
45o
45o
11
2Ratio of the sides in a 45:45:90 Right Triangle is 1: 1: √2
Find the lengths of the sides
9x
12
9 2x
9y
119y
s
9s 9 2x 9y
s
2s
Find the lengths of the sides
3 2u
21
2 3 2u 3u
3 2v
21
2 3 2v 3v
s s
2s
3 2 2s2 23 s
3u 3v
Find the length of the sides
5v
21
2 5v 52
v
Rule: NO RADICALS IN THE DENOMINATOR!!!
22
5 22
3.54
Rationalize the denominator
Find the length of the sides
52
v s
Rule: NO RADICALS IN THE DENOMINATOR!!!
22
5 22
3.54
Rationalize the denominator
s
s2s
5 2s2 2
52
s
30-60-90 TrianglesEquilateral Triangle
60o
30o
1 1
230o
60o
2
2 221 2h 21 4h
2 3h 3h
30o
60os
2s3s
Isosceles Right Triangles
Ratio of the sides in a 30:60:90 Right Triangle is 1: √3: 2
30o
60o1
23
Find the lengths of the sides
3x
126x
3y
13
3 35.20
yy
3 3y 3s
2 3x
6s
s 3s
2s
5.20y
Find the lengths of the sides
3x
126x
3y
13
3 35.20
yy
7 3s3
7 323
m
33
7 33
4.04
14 33
8.08
s
3s
2s
3
73
s
n s
7 33
n
Solve for x.11y
12
11 2y
11 2x
13
11 626.94
yy
11 2
Did you meet today’s objective? How do special right triangles relate to
Pythagorean Theorem?