Theorems
Theorems
Ratios
Ratios & Laws
100
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
What is the Pythagorean theorem?
100
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments.
What is the geometric mean (altitude) theorem? (Heartbeat method).
100
tan A = length of opposite leg/length of adjacent leg
What is the tangent ratio?
100
If cos A = z, then cos-1z = angle A.
What is inverse cosine?
200
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
What is the converse of the Pythagorean theorem?
200
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
What is the geometric mean (leg) theorem? (Boomerang method).
200
sin A = length of opposite leg/length of hypotenuse
What is the sine ratio?
200
If triangle ABC has sides of length a, b, and c as shown, then sinA/a = sinB/b = sinC/c.
What is law of sines?
300
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.
What is theorem 7.3?
300
In a 45-45-90 triangle, the hypotenuse is root two times as long as each leg. Hypotenuse = leg • root 2
What is the 45-45-90 triangle theorem?
300
cos A = length of adjacent leg/length of hypotenuse
What is the cosine ratio?
300
If triangle ABC has sides of length a, b, and c, then: a squared = b squared + c squared - 2bc cos A b squared = a squared + c squared - 2ac cos B c squared = a squared + b squared - 2ab cos C
What is law of cosines?
400
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle.
What is theorem 7.4?
400
In a 30-60-60 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is root three as long as the shorter leg.
What is the 30-60-60 triangle theorem?
400
If tan A = x, then tan-1x = angle A.
What is inverse tangent?
500
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
What is theorem 7.5?
500
If sin A = y, then sin-1y = angle A.
What is inverse sine?
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