Triangle Theorems
A segment that connects the midpoints of two sides of a triangle has this relationship with the third side.
(What is parallel and half the length?)
These angles in a parallelogram are always equal.
(What are opposite angles?)
If two triangles have this set of corresponding parts equal, they must be similar.
(What is two angles (AA)?)
This famous theorem states
a^2+b^2=c^2
(What is the Pythagorean Theorem?)
This ratio is defined as opposite over adjacent.
(What is tangent?)
When this is drawn to the hypotenuse of a right triangle, it creates three similar triangles.
(What is the altitude/height?)
The measure of consecutive angles in a parallelogram always add up to this.
(What is 180°?)
When two triangles are similar with scale factor r, their areas have this ratio.
(What is
r^2
?)
In a 45-45-90 triangle, this is the relationship between the legs.
(What is they are equal?)
Sine and cosine of complementary angles have this relationship.
(What are they are equal?)
This inequality shows a triangle is obtuse:
(What is the Pythagorean Inequality?)
This special parallelogram has perpendicular diagonals that bisect its angles.
(What is a rhombus?)
Three parallel lines cut by two transversals create segments with this relationship.
(What is proportional?)
This is created when an altitude is drawn to the hypotenuse of a right triangle.
(What is a geometric mean?)
This special angle has both a sine and cosine value of
sqrt2/2
(What is 45°?)
In a 30-60-90 triangle, the hypotenuse is always this multiple of the shortest side.
(What is 2?)
This is the only condition needed to prove a quadrilateral is a parallelogram when paired with parallel sides.
(What is congruent sides?)
If two triangles have side lengths in the ratio of
3/5
, then their perimeters will be in this ratio, but their areas will be in this ratio.
(What is
3/5
for perimeters and
9/25
for areas?)
This special right triangle is formed by cutting an equilateral triangle in half.
(What is a 30-60-90 triangle?)
This angle is formed between a line of sight and the horizontal plane when looking up.
(What is angle of elevation?)
This theorem states that the line segment bisecting an angle of a triangle divides the opposite side into segments proportional to the lengths of the other two sides.
(What is the Triangle Angle Bisector Theorem?)
In a rectangle, these are always congruent and bisect each other.
(What are diagonals?)
When proving triangles similar using SAS~, this must be included in the similarity statement.
(What is the included angle?)
If the shortest leg in a 30-60-90 triangle is x, the longest leg is this.
(What is
xsqrt3
?)
When finding an unknown angle in a right triangle using inverse trig functions, this function is used when you know the adjacent and hypotenuse sides.
(What is inverse cosine?)