WARM UP

• Pass out progress reports!

• Get a Calendar from the front!

RIGHT TRIANGLES AND THE PYTHAGOREAN THEOREM

ON GRAPH PAPER… • Draw a rectangle

• Label the dimensions a and b

• Cut out 4 rectangles that are a x b

• Label the sides a and b-inside the rectangle

• Cut each rectangle on one diagonal

• Label your new sides as c

• Cut out 3 squares: one with sides a, one with sides b, and one with sides c

WHAT NOW…

• Make 2 groups

• 4 triangles and the 2 smaller squares

• Four triangles and the big square

• Make a big square from each group, no overlapping parts (you will have 2 squares)

QUESTIONS:• What is each side length?

• What is the area of each square?

• What can you say about the relationship of the 3 squares?

• Use a ruler, measure sides a, b and c. Plug these values into your expression, does it work?

HYPOTENUSE

• Longest Side

• Across from the RIGHT ANGLE

• Only in right triangles

THE PYTHAGOREAN THEOREM

• If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

a2 + b2 = c2

SOLVE FOR THE VARIABLE-IN SIMPLEST RADICAL FORM

• y = 60 y = 5√5

• 2√77 2√19

• A rhombus has diagonals of 12 cm and 20 cm. What is the perimeter of the rhombus? in simplest radical form

• A window washer has an 18-ft ladder. He needs to reach the bottom of a window 16 feet of the ground. How far out from the building should the base of the ladder be? Round to the nearest tenth of a foot.

CONVERSE OF THE PYTHAGOREAN THEOREM

• If the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse, then the triangle is a right triangle.

• a2 + b2 = c2

IS IT A RIGHT TRIANGLE?

• Yes Yes No

A2 + B2 < C2 THINK IN TERMS OF C

• If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is OBTUSE.

A2 + B2 > C2 THINK IN TERMS OF C

• If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is ACUTE.

CLASSIFY THE TRIANGLE

• 9, 11, 16

• 10, 12, 14

• 24, 70, 74

• Obtuse

• Acute

• Right

CAN ANY 3 LENGTHS MAKE A TRIANGLE?• 1, 2, 3

• 2, 3, 4

• 3, 4, 8

• Cut your paper into pieces that have a length of 1, 2, 3, 4, & 8 cm.

• Try to create the triangle given.

TRIANGLE SIDES

• To make a triangle, the two smaller sides must have a SUM that is GREATER than the third side.

IS THIS A TRIANGLE??

• 2, 4, 5

• 6, 7, 14

• 3, 6, 9

• YES

• NO

• NO

AREA OF A TRIANGLE

• Half the product of a base and the corresponding height

• A = ½ bh

FIND THE AREA

56ft2 13.75ft2

FINDING AREA USING TRIANGLE TRIG

• Given SAS, the area of the triangle is half the product of the lengths of two sides and the sine of the included angle.

• A = ½ bc(SinA)

• A = ½ ac(SinB)

• A = ½ ab(SinC)

TRY SOME

11.1 m2 35.9 in2 86 in2

HOMEWORK

Worksheet