special right triangles. 45-45-90 right isosceles triangle leg hypotenuse legs are congruent...

Special Right Special Right Triangles Triangles

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Page 1: Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

Special Right Special Right TrianglesTriangles

Page 2: Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

45-45-9045-45-90Right Isosceles TriangleRight Isosceles Triangle

Leg

Hyp

oten

e Legs are congruent

Hypotenuse =

Legs =

2Leg

Hypotenuse

2Hyp

45-45-9045-45-90Right Isosceles TriangleRight Isosceles Triangle

21 2124221 26

262

212

64 64

383243224124264

LegLeg LegLeg HypHyp

11 11

3333

1212

Page 4: Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

45-45-9045-45-90Right Isosceles TriangleRight Isosceles Triangle

Leg

1-If the perimeter of the square is 28, what is the length of the diagonal?

2- If the diagonal has a length of 12, what is the perimeter of the square?

Area?

The diagonal of a square is the Hypotenuse of two isosceles right triangles.

1- Perimeter = 28 4x = 28 x = 7 Leg = 7 Hyp = 7 2

2- Diagonal = 12

Leg = 12÷ 2 = 6 2

P = 4(6 2) =24 2

A = 6 2·6 2 = 72

Page 5: Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

30-60-9030-60-90

LongLeg

ShortLeg

Hyp

oten

eKnow the Short Leg (SL):

Hypotenuse = 2 · SL Long Leg =

Know Hypotenuse:

Short leg = ½ Hypotenuse

Know Long Leg (LL): Short leg =

3LL

30°

60°

3 SL

Page 6: Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

30-60-9030-60-90

ShortShortLegLeg

Long Long LegLeg

HypHyp

312

11 2233 66

4422

121266

1212 2424

1212

34 38

312

312 34

Page 7: Special Right Triangles. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

30-60-9030-60-90When you draw the altitude of an equilateral triangle, you create two 30-60-90 triangles.

The triangle side length is the hypotenuse of the 30-60-90.

Half of the side length is the short leg of the 30-60-90.

The altitude, then, is half the triangle side times the square root of 3.

60°

30°

Find the hypotenuse in a right triangle with legs a = 3 and b = 4. 55 Exercise

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