Download Rules for Triangles

Rules for Triangles
1.
Triangles are described by two things – their sides or their angles. Triangles do not have diagonals.
2.
Triangles can be described by how many sides are congruent (congruent means exactly the length):
a) Equilateral: All sides are congruent.
b) Isosceles: Only two sides are congruent.
c) Scalene: No sides are congruent.
3.
Triangles can be described by their interior angles:
a) Acute: Each interior angle measures less than (<) 90 degrees.
b) Right: One right angle (90 degrees). The other two angles will be acute.
c) Obtuse: One angle more than (>) 90 degrees. The other two angles will be acute.
4.
How triangles are described:
a) Describe triangles by their sides and angles. It doesn’t matter if you put sides or angles first.
b) Examples (there are more possible arrangements than shown):
1) Right Isosceles: a right angle with two equal sides.
2) Right Scalene: a right angle with no equal sides.
3) Obtuse Isosceles: an obtuse angle with two equal sides.
c) It is not possible to have a Right Equilateral or an Obtuse Equilateral.
d) All equilateral triangles are also acute triangles.
5.
Other facts about triangles:
a) There are no diagonals in any triangle.
b) All three of interior angles added together equal 180 degrees – always, all the time.
c) When measuring the sides, any two sides (when added together) MUST be longer than the remaining side.
d) If three angles are equal then three sides are equal and vice versa (equilateral).
e) If two angles are equal then two sides are equal and vice versa (isosceles).
f) If no angles are equal then no sides are equal and vice versa (scalene).
g) Acute angles are less (<) than 90 degrees.
h) Right angles are exactly 90 degrees.
i) Obtuse angles are greater than (>) 90 degrees and less than (<) 180 degrees.
j) Straight angles are exactly 180 degrees.
k) All triangles have two acute angles; the remaining angle may be acute, right, or obtuse.
l) Two or more triangles are congruent if and only if their interior angles and sides are identical. Two or more
triangles with identical interior angles but with different length sides are called similar triangles AND each corresponding
side from one triangle to the other triangle must be proportional.
m) The apothem is the distance from the center of an equilateral triangle to the midpoint of a side (must form a right angle).
n) Each interior and corresponding interior angle adds to 180 degrees. Each exterior angle must be 360°/n (n = number of
sides).