7.4 Special Right Triangles OBJECTIVE: To use relationships among the sides in special right triangles on a piece of paper draw 3 squares with sides of 10, 8, and 2 (cm) This should take 3-4 minutes max!

Quiz

now draw the other diagonals Draw the diagonal on the 10 cm square. Describe the angle measures of the square. Explain what the diagonal represents. What transformation happens by ‘folding’ along the diagonal? What is the line of symmetry doing through the 90° angles? What are the angles in one of those triangles? If the diagonal is a line of symmetry (line of reflection), are the 2 resulting right triangles congruent?. What other type of triangle is being formed besides a right triangle?) each is 90° it is a line of symmetry A reflection cutting them in half – it is an angle bisector. 45-45-90 Yes, because the triangle has been reflected over the line of symmetry. Isosceles triangle now draw the other diagonals

Is there a pattern, you suspect . . . - Measure one side of each of your triangles, - then calculate the hypotenuse using Pythagorean theorem – simplify your answers, - then check it by measuring the diagonals 10 10 10 8 8 8 2 2 2 Is there a pattern, you suspect . . .

Ws homework 8 (triple) 4.94 Acute Not a tiangle 14 29.84 feet

Homework P. 444 13. right triangle 23. triangle, obtuse 27. right 9. ~9.14 in. 13. 48 sq. cm 28. 6 29. 31. about 127 feet 34. a)about 197 feet B) about 19 trees C) about $228 P. 444 13. right triangle 23. triangle, obtuse 27. right 33. 12 < x < 16

ISOSCELES RIGHT TRIANGLES notes **45-45-90** ISOSCELES RIGHT TRIANGLES leg = hypotenuse

Solving Special Right Triangles using the ratios for the sides 1 y 20 x Find x and y. X = 20

Set up proportion to solve special right triangles 1 1 7 y y x x Find x and y. Find x and y. X = 7

Set up proportion to solve special right triangles 1 1 18 y y x x Find x and y. Find x and y. X = 29

Solving 45-45-90 x2 = 8 x = 42 8 X

“Look OUT for” squares cut by a diagonal m h 18 12 k square r 36 (A 45-45-90 Triangle)

Elaborate: 1. The perimeter of a square is ft. Find the length of the diagonal of the square as well as the length of each side of the square. 2. Given the square shown below, find the perimeter and area. 36 cm

In class practice work 1-5, 12,13, 14 A leg of a 45-45-90 triangle is 3in. Find the length of the hypotenuse. 2. Calculate the approximate length of a diagonal of a square with sides of 8 cm. 3. In ΔABC, <A is a right angle and m<B = 45°. If AB = 30 feet, find AC.

. . . on the back of original paper Use a ruler to draw a line segment of 12 cm length near the bottom edge of you piece of paper. Use a protractor to measure a 60 ° angle at one end. Measure from the vertex of the angle (that's the pointy bit) along the new line until it’s length matches the line segment from part one. Mark this spot. Connect this point to the unattached end of the first line segment. You should now have an equilateral triangle. Step 1 Step 2 Step 3

Construct the perpendicular bisector of the triangle 5. Arrange the sides of ∆ABD from smallest to largest. 1. Classify the triangle by it’s sides and by it’s angles. B 6. What is the length of AB? AD? 2. What are the angle measures of each of the triangle’s angles. 7. What is the length of BD? How can we verify? 3. What does the altitude of this triangle do to the triangle and it’s angles? A C 4. What other special segments are BD?. D 8. Using Pythagorean Thm find the simplified length of BD . . .

30°-60°-90° Triangles In a 30°-60°-90° Triangles, the hypotenuse is twice the length of the short leg and the long leg is times as long as the short leg. 60 2x 4 2 x 30

**30-60-90** short leg * = long leg short leg * 2 = hypotenuse

Solving Special Right Triangles using the ratios for the sides 30° 60° 1 2 2 1 30 60 b 2 a² + b² = c² 1² + b² = 2² b² = 4-1 b² = 3 b =

Set up proportion to solve special right triangles 30° 60° 1 2 30° 60° 1 2 12 y x y x 10 Find x and y. Find x and y. 2x = 12(1) X =6 X = 20

Set up proportion to solve special right triangles 30° 60° 1 2 30° 60° 1 2 y y x x Find x and y. Find x and y.

Set up proportion to solve special right triangles 30° 60° 1 2 y x Find x and y.

Elaborate: 1. The perimeter of an equilateral triangle is 96 ft. Find the length of each side of the triangle as well as the altitude. 2. Given the rectangle shown below, find the diagonal length, vertical side length, perimeter and area. 60 24 Perimeter = Area =

Ones to look for: 40 n m Equilateral triangle (A 30-60-90 Triangle)

In class practice 6. The length of the hypotenuse of a 30-60-90 triangle is 10 m. Find the length of the side opposite the 30° angle.   7. The shorter leg of a 30-60-90 triangle is 3.4 feet long. Find the perimeter. 8. The long leg of a 30-60-90 is 27m. Find the length of the short leg and the hypotenuse. 9. In ΔABC, <A is a right angle and m<B = 30. If AB = 18 feet, find BC. 10. One angle of a right triangle is 60°. The side opposite this angle is 7. Find the length of the two remaining sides.

Classwork, finish Practice Ws 7.4 special right triangles

classwork 5 m 10.2 + 3.4 feet 9 + 18 12 3 , 6 Alt.=12; per = 24 6.2733 9 + 18 12 3 , 6 Alt.=12; per = 24 6.2733 1.2 13.5 = 40.5cm 9 in. 23.1 ft 3 ~5.196 cm 6 ~10.39 43.5 feet x=1.5, y= Homework: WS 7.4 special right triangles

WS 7.4 Special Rights a=22 + 4 b=8 m=2.25 x=2 ; y=2 x = 4; y = wire = 12 ; ht = 12 F; every to some T F; either to shorter F 60° to 30° 24 42 30° 9 36 25.5 -8.5

classwork 1.2 km 4.999 feet (or 5’) 8.395 ~11.872 in. 127.3 feet 8485.2 meters 8 3 in. 16 cm 30 feet 8 10 or both 5 7 14 .707 inch or 2 ~7.483 feet Book work: Pg. 461: 3, 11, 17, 33 Pg. 909: 28, 30, 32

Book work Pg. 461: 7 11. t=4 ; u = 7 33. 45-45-90 for all triangles c 10 Pg. 461: 7 11. t=4 ; u = 7 33. 45-45-90 for all triangles b. C. 1.5 in x 1.5 in. Pg. 909: 28. x=7; y= 7 30. a = b= 9 32. s = t =