Study your flashcards anywhere!
Download the official Cram app for free >
 Shuffle
Toggle OnToggle Off
 Alphabetize
Toggle OnToggle Off
 Front First
Toggle OnToggle Off
 Both Sides
Toggle OnToggle Off
 Read
Toggle OnToggle Off
How to study your flashcards.
Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key
Up/Down arrow keys: Flip the card between the front and back.down keyup key
H key: Show hint (3rd side).h key
A key: Read text to speech.a key
12 Cards in this Set
 Front
 Back
Geometric mean

If a, b and x are positive numbers with a/x=x/b, then x is the geometric mean between a and b


Complete the theorem: If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed...

are similar to the original triangle and to each other.


Complete the corollary: When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude...

is the geometric mean between the segments of the hypotenuse


Complete the corollary: When the altitude is drawn to the hypotenuse of a right triangle, each leg...

is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg


Pythagorean Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.


Converse of the Pythagorean Theorem

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.


Common right triangle lengths

(3,4,5), (6,8,10), (9,12,15), (12,16,20), (15,20,25)/(5,12,13), (10,24,26), (15,36,39), (20,48,52), (25,60,65)/(8,15,17), (16,30,34), (24,45,51), (32,60,68), (40,75,85)/ (7,24,25), (14,48,50), (21,72,75), (28,96,100), (35,120,125)


Complete the theorem: If c^2=a^2+b^2, then...

the measure of angle c=90 & triangle ABC is a right triangle


Complete the theorem: if c^2<a^2+b^2, then...

the measure of angle c<90 and Triangle ABC is an acute triangle


Complete the theorem: If c^2>a^2+b^2, then

the measure of angle C>90 and Triangle ABC is an obtuse triangle


45º45º90º Theorem

In a 45º45º90º triangle, the hypotenuse is the square root of 2 times as long as the leg


30º60º90º Theorem

In a 30º60º90º triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg.
