45-45-90 right triangles

1
45-45-90 right triangles

• Some right triangles are used so frequently that
  it is helpful to remember some of their
  properties.
• These triangles are called special right
  triangles
• The 2 most common are the 45-45-90 triangle and
  the 30-60-90 triangle.
• Since the 45-45-90 triangle has 2 angles with
  equal measures, it is also an isosceles right
  triangle

2
Properties of a 45-45-90 triangle side lengths

• In a 45-45-90 right triangle, both legs are
  congruent and the length of the hypotenuse is the
  length of the leg multiplied by

3
Finding side lengths in a45-45-90 triangle

• Use the properties to find the length of the
  hypotenuse of the triangle
• The length of the hypotenuse is equal to the
  length of the leg times

45
2 in
4
Finding side lengths

• Find the length of a leg of the triangle
• The length of the hypotenuse is the length of the
  leg times

3 ft
45
5
Finding perimeter of a 45-45-90 triangle

• Find the perimeter
• 12 12 ? Perimeter

12 yd.
45
6

• Though it is faster to use the properties of
  45-45-90 triangles to find unknown lengths, the
  Pythagorean theorem can still be used

7
Applying Pythagorean theorem

• Find the length of the missing sides using
  Pythagorean theorem

125 ft
45
8
review

• 1. Find the length of the hypotenuse in a
  45-45-90 triangle with a leg of 31 yd.
• 2.Find the length of a leg in a 45-45-90 triangle
  if the hypotenuse is 63 m.
• 3. Find the perimeter of a right triangle with
  an45 degree angle and a leg of 18 in.
• 4. A square building has a diagonal of 150 feet.
  What would be the square footage of 1 floor of
  the building.