Special Triangles

Question 0

Isosceles Triangles

Answer 0

Two sides are the same length, and the angles facing those sides are equal.

Question 1

Equilateral Triangles

Answer 1

All interior angles are 60 degrees, and all sides are the same length.

Question 2

Right Triangles

Answer 2

Right Triangles contain a 90 degree angle. The sides that form the 90 degree angle are the legs; the side facing the 90 degree angle is the hypotenuse. The sides are related by the Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Question 3

3:4:5 Right Triangle

Answer 3

These right triangles all have side lengths in the ratio 3:4:5. If you multiply 3, 4, and 5 each by the same number, you get a ratio equivalent to 3:4:5. For example, 6:8:10 is equivalent to 3:4:5.

Question 4

5:12:13 Triangles

Answer 4

Right triangles whose sides are in the ratio 5:12:13 also occur frequently. Keep an eye out for side lengths that are multiples of 5:12:13. For example, 10:24:26.

Question 5

45-45-90 Right Triangles (Isosceles Right Triangles)

Answer 5

These triangles have side lengths in the ratio 1:1:sqrt(2). Note that the legs have the same length. An isosceles right triangle is formed when a square is divided in half by one of its diagonals.

Question 6

30-60-90 Right Triangles

Answer 6

These triangles have side lengths in the ratio 1:sqrt(3):2. When an equilateral triangle is divided in half, the result is a 30-60-90 triangle.

Question 7

True or False: The sum of the lengths of any two sides of a triangle are always greater than the third side.

Answer 7

True