Math Handbook - Geometry

Flashcards from Geometry Lecture Notes

Intersecting Chords Theorem

The angle made by two chords that intersect inside a circle is half the sum of the two opposite intercepted arc measures.

Intersecting Secants Theorem (segments)

The product of the outer segment length of the first secant multiplied to its total segment length is equal to the product of the outer segment length of the second secant multiplied to its total segment length.

Intersecting Tangents Theorem

Tangent segments of a circle coming from the same point are always equal.

Intersecting Chords (bisected)

The product of the segments of the first bisected chord is equal to the product of the segments of the second bisected chord.

Intersecting Secants Theorem (angles)

The angle made by two secants that intersect outside a circle is half the difference between the intercepted arc measures.

Pythagorean Theorem

A² + B² = C², where A and B are the legs of the triangle, while C is the hypotenuse.

Pythagorean Triples

Common ratios in right triangles: 3x:4x:5x, 5x:12x:13x, x:x:x√2, x:x√3:2x

x:x:x√2 Pythagorean Triple

Used for any isosceles right triangle.

x:x√3:2x Pythagorean Triple

Used for 30°-60°-90° triangles.

Volume of a sphere

V = 4/3πr³

Total surface area of a cylinder

total surface area = 2πr² + 2πrh

Total Surface Area of a Cone

total surface area = πr² + πrh

Total surface area of a sphere

total surface area = 4πr²

Volume of a cube

V = s³

Volume of a rectangular prism

V = lwh

Volume of a triangular prism

V = 1/2bhl

Volume of a cylinder

V = πr²h

Complementary Angles

Add up to 90 degrees

Supplementary Angles

Add up to 180 degrees.

Vertical Angles

Angles that are equal

Exterior Angle Theorem

An exterior angle is equal to the sum of the two remote interior angles.

Angle Relationships (Parallel Lines)

Corresponding angles, alternate interior angles, and exterior angles are equal.

Similar Triangles

Corresponding sides of similar triangles are proportional.

Triangle Angle Sum Theorem

The sum of the measures of all angles of any triangle is 180°.

Equilateral Triangle

Has three congruent sides and three congruent angles.

Central Angle

Has its vertex at the center of a circle and endpoints on the circumference; its degree measure is equal to that of its intercepted arc.

Inscribed Angle

Has its vertex and endpoints on the circumference; its degree measure is half that of its intercepted arc.

Isosceles Triangle Theorem

The angles opposite two equal sides are also equal.

Triangle Inequality Theorem

The sum of any two sides is always greater than the third side.

Perimeter of a Square

P = 4s (where s is the length of each side)

Perimeter of a Rectangle

P = 2l + 2w (where l = length and w = width)

Circumference of a Circle

C = 2πr (where r = radius)

Area of a Square

A = s² or A = d²/2 (where d = diagonal)

Area of a Parallelogram

A = bh

Area of a Trapezoid

A = 1/2(b₁ + b₂)h

Total Surface Area of a Cube

total surface area = 6s²

Area of a Rectangle

A = lw

Area of a Triangle

A = 1/2bh (where b = base and h = height)

Area of a Circle

A = πr²