Geometry

The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education.

Martin Luther King, Jr.

Today:• 8.3

Instruction• Practice

8.3 Special Right TrianglesObjectives:

1. Identify special right triangles

2. Use special right triangles to solve for missing side lengths

 

Vocabulary: 30:60:90, 45:45:90

Content Standards

G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Mathematical Practices

1 Make sense of problems and persevere in solving them.

7 Look for and make use of structure.

You used properties of isosceles and equilateral triangles.

• Use the properties of 45°-45°-90° triangles.

• Use the properties of 30°-60°-90° triangles.

What type of triangle is ΔABC?

If AC = 1, find AB.

A B

C

A B

C

A right isosceles or 45:45:90 triangle is known as a special right triangle.The sides will always be in the ratio 1:1:It will always have two congruent legs and the hypotenuse will equal times the leg.

30°

60°

Another special right triangle is a 30:60:90 triangle.The sides will always be in the ratio 1 :: 2It will always have one short leg, the hypotenuse will equal the short leg times 2 and the long leg will equal times the short leg.

5x

y

Find the value of x and y.

45°

Helpful Hints:• Label all angles and locate the short leg.• Find the value of the short leg.• Find the value of remaining side(s) from the

short leg.

60°

yx

 

Find the value each variable.

m

n

45°

60°

ba

12

7 6

Geometry

The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education.

Martin Luther King, Jr.

Assignment:P. 562 #9-25

oddCALCULATOR

WITHSIN ASAP

Geometry

The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education.

Martin Luther King, Jr.

Today:• Homework

Check• 8.3 More

Practice

Homework Quiz

Take out a piece of notebook paper label it CHAPTER 9 HOMEWORK QUIZ.

Write down the date (3/5), then write out p 562 # 19 (INCLUDING PICTURE!!!), your work and your answer.

A. Find x.

A. 3.5

B. 7

C.

D.

Find b.

A.

B. 3

C.

D.

BOOKENDS Shaina designed 2 identical bookends according to the diagram below. Use special triangles to find the height of the bookends.

A.

B. 10

C. 5

D.

Find x and y.

A.

B.

C.

D.

The hypotenuse of a 30°-60°-90° triangle measures

inches. What is the length of the side

opposite the 30° angle?

A. 10 in.

B. 20 in.

C.

D.

Find the value of x and y. Write answers in simplest radical form.

x

Find the value of each variable. Write answers in simplest radical form.

Geometry

The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education.

Martin Luther King, Jr.

Assignment:P. 563 #29-38CALCULATOR

WITHSIN ASAP

B. Find x.

A.

B.

C. 16

D. 32

Find BC.

A. 4 in.

B. 8 in.

C.

D. 12 in.

A. (–1, 3)

B. (–3, 3)

C. (5, 3)

D. (6, 2)

ΔMNP is a 45°-45°-90° triangle with right angle P. Find the coordinates of M in Quadrant II for P(2, 3) and N(2, 8).

The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle.

A. in.

B. 12 in.

C. 14 in.

D. in.

A. 15 cm

B. 30 cm

C. 45 cm

D. 60 cm

The length of the diagonal of a square is centimeters. Find the perimeter of the square.

You work for the village and you are commissioning new road sign. A typical yield sign is an equilateral triangle with a side length of 36 in. Estimate how much metal you will need to make 75 signs.

h

18 in.

36 in.

Two companies have made offers to supply the metal. One is offering a rate of $0.40 per square foot. The other is offering 40,000 square inches for $100. Which is a better deal?

Geometry

The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education.

Martin Luther King, Jr.

Assignment:P. 566 #51-

59CALCULATO

R WITHSIN ASAP