why does the line y = x only have one slope? what is true about all of the triangles? how does this...

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?