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 Triangles Day 3 – Special Right Triangles

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 Triangle

Answers to Homework 11) (12 √3 ) 2 = = 576 Right Triangle 12) ( √60 ) 2 = > 64 Acute Triangle 13) PR 2 + RQ 2 = PQ 2 ( √10 ) 2 + ( √20 ) 2 = ( √26 ) > 26 Acute Triangle 14) (a) 2 + (b) 2 = (c) 2 (2n) 2 + (n 2 - 1) 2 = (n 2 + 1) 2 4n 2 + n n = n n n = 2 n Yes, this method will work because both sides of the equation are equal. 15) StatementsReasons 1. AB = 4, BC = 2, AC = √10 1. Given 2. AB 2 + AC 2 = BC 2 2. Pythagorean Theorem ( √10) 2 = Substitution < 164. 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

Isosceles Right Triangles 45 o Ratio of the sides in a 45:45:90 Right Triangle is 1: 1: √2

Find the lengths of the sides

Find the length of the sides Rule: NO RADICALS IN THE DENOMINATOR!!! Rationalize the denominator

Find the length of the sides Rule: NO RADICALS IN THE DENOMINATOR!!! Rationalize the denominator

Triangles Equilateral Triangle 60 o 30 o 60 o 30 o 60 o

Isosceles Right Triangles Ratio of the sides in a 30:60:90 Right Triangle is 1: √3 : 2 30 o 60 o

Find the lengths of the sides

Solve for x.

Did you meet today’s objective?  How do special right triangles relate to Pythagorean Theorem?