Unit 8 Flashcards
In a right triangle with an altitude coming from the right angle, what is the geometric mean formula using h (the altitude)?
x / h = h / y
In a right triangle with an altitude coming from the right angle, what is the geometric mean formula using the legs (a or b)?
x /a = a / c or y /b = b / c
The Pythagorean Theorem only works with what type of triangle?
A right triangle
Give the Pythagorean Theorem
a² + b² = c²
What must c be in the Pythagorean Theorem?
The hypotenuse
Give the Pythagorean Theorem in 3D
d² = l² + w² + h²
What is the requirement about ‘c’ when using the Converse of the Pythagorean Theorem to determine the type of triangle with given side lengths?
c must be the longest side
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if c² < a² + b² ?
Acute
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if c² = a² + b² ?
Right
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if c² > a² + b² ?
Obtuse
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if a + b < c?
Not a triangle
Give the “names” of the 2 special right triangles.
45°-45°-90° and 30°-60°-90°
What is another name (the proper name) for a 45°-45°-90° triangle?
Isosceles right triangle
In a 45°-45°-90° triangle, how do you go from leg to hypotenuse?
Multiply by √2
Which is the most important side to find in a 30°-60°-90° triangle?
The short leg
In a 45°-45°-90° triangle, how do you go from hypotenuse to leg?
Divide by √2
In a 30°-60°-90° triangle, which leg is the “long leg”?
The one opposite the 60º angle.
In a 30°-60°-90° triangle, how do you go from short leg to hypotenuse?
Multiply by 2
In a 30°-60°-90° triangle, how do you go from short leg to long leg?
Multiply by √3
In a 30°-60°-90° triangle, how do you go from hypotenuse to short leg?
Divide by 2
In a 30°-60°-90° triangle, how do you go from long leg to short leg?
Divide by √3
In a 30°-60°-90° triangle, how do you go from long leg to hypotenuse?
You don’t
In a 30°-60°-90° triangle, how do you go from hypotenuse to long leg?
You don’t
Complete the pythagorean triple: 7,___,25
7, (24), 25
