Triangles Flashcards
The largest angle is ________.
opposite the largest side
How many degrees are in an equilateral?
180, where every side is 60°
What is a 45-45-90 triangle?
It is a special right triangle and an isosceles. Its two legs are equal.
What are the sides of a 45-45-90 triangle?
x, x, and x√2
(where the length of the legs are x, and the hypotenuse is √2 times x)
The smallest angle is _________.
opposite the smallest side
What is a 30-60-90 triangle?
It is a special right triangle that can be proved by halving an equilateral triangle.
What is one rule for solving 30-60-90 triangles?
The ratio of the angles cannot be used to determine the ratio of the sides.
What are the sides of a 30-60-90 triangle?
x, x√3, and 2x
where the short leg is x, the hypotenuse is 2x, and the long leg is x√3
What are the triangle postulates that state what is required to prove that a triangle is congruent?
SSS / SAS / AAS / ASA. These conditions must be met for both triangles in order to prove congruence.
What are the properties of congruent triangles?
They have the same angles and side lengths.
What are the properties of similar triangles?
They have the same angles. The ratios of their sides are proportional as well as their perimeters.
In what ways can you prove that a triangle is similar?
Checking if their side lengths are proportional or if their angles are the same. Either is sufficient to prove it is similar.
What is one rule for considering similar triangles?
As long as they have the same angles, the location of the angles themselves don’t matter, unlike the proportional side lengths.
What is an obtuse triangle?
There’s one angle that measures greater than 90 degrees.
What is a right triangle?
There’s one angle that measures exactly 90 degrees.
