Geometry Formulas and Theorems

Flashcards based on lecture notes about geometry, including the Pythagorean theorem, trigonometric ratios, special right triangles, midsegments, polygons, and circle properties.

Obtuse Triangle Condition

If c² > a² + b², then the triangle is an obtuse triangle.

Pythagorean Theorem

If a right triangle has legs with measures a and b and hypotenuse with measure c, then a² + b² = c².

Converse of Pythagorean Theorem

If c² = a² + b², then the triangle is a right triangle.

Acute Triangle Condition

If c² < a² + b², then the triangle is an acute triangle.

sin A

leg opposite / hypotenuse

cos A

leg adjacent / hypotenuse

tan A

leg opposite / leg adjacent

45-45-90 Triangle Ratio

In a 45-45-90 triangle, the hypotenuse = leg * √2

30-60-90 Triangle Ratio

In a 30-60-90 triangle, the hypotenuse = 2 * shorter leg and longer leg = shorter leg * √3

Triangle Midsegment Theorem

midsegment = 1/2 * base

Trapezoid Midsegment Theorem

midsegment = (base₁ + base₂) / 2

Sum of interior angle measures of a polygon

(n - 2) * 180°

Measure of each interior angle of a regular polygon

(n - 2) * 180° / n

Measure of each exterior angle of a regular polygon

360° / n

Inscribed Angle Theorem

x = n / 2

Angle formed by 2 Chords Theorem

x = 1/2 * (m + n)

Chords Theorem

a * b = c * d