Summer Geo Vocab/Formulas

Ruler Postulate

Points on lines map to numbers.

Sum of Interior Angles

(n-2) x 180

Segment Addition Postulate

Part plus part equals whole.

Protractor Postulate

Angles measure from 0° to 180°.

Angle Addition Postulate

Adjacent angles add up together.

Linear Pair Postulate

Adjacent line angles equal 180°.

Vertical Angles Theorem

Intersecting opposite angles are congruent.

Corresponding Angles Postulate

Parallel lines create matching positions.

Alternate Interior Angles Theorem

Inner Z-shaped angles match exactly.

Alternate Exterior Angles Theorem

Outer opposite angles match exactly.

Consecutive Interior Angles Theorem

Inner same-side angles add to 180°.

SSS Congruence Postulate

Three matching sides create congruence.

SAS Congruence Postulate

Two sides and trapped angle match.

ASA Congruence Postulate

Two angles and trapped side match.

AAS Congruence Theorem

Two angles and next side match.

HL Congruence Theorem

Right triangle hypotenuse and leg match.

Triangle Sum Theorem

Internal angles always total 180°.

Isosceles Triangle Theorem

Equal sides mean equal base angles.

Exterior Angle Theorem

Outer angle equals remote interior sum.

AA Similarity Postulate

Two matching angles mean similar triangles.

SSS Similarity Theorem

Three proportional sides mean similar triangles.

SAS Similarity Theorem

Two proportional sides, one matching angle.

Pythagorean Theorem

Legs squared equal hypotenuse squared (a² + b² = c²).

Parallelogram Opposite Sides Theorem

Opposite sides share equal lengths.

Parallelogram Opposite Angles Theorem

Opposite corners share equal measures.

Polygon Interior Angles Theorem

Interior total equals (n - 2) × 180°.

Tangent Line Theorem

Radius meets tangent at 90°.

Inscribed Angle Theorem

Corner angle equals half the arc.

Area Addition Postulate

Total area sums non-overlapping regions.

Cavalieri's Principle

Matching cross-sections yield identical volumes.

Point

A location in space with no size or dimension.

Line

A straight path extending infinitely in two opposite directions.

Plane

A flat, two-dimensional surface extending infinitely.

Segment

A part of a line with two distinct endpoints.

Ray

A part of a line with one endpoint extending infinitely.

Collinear

Points that lie on the exact same line.

Coplanar

Points or lines lying in the same plane.

Midpoint

A point that divides a segment into two equal parts.

Segment Bisector

A line, ray, or segment intersecting at a midpoint.

Acute Angle

An angle measuring strictly between 0° and 90°.

Right Angle

An angle measuring exactly 90°.

Obtuse Angle

An angle measuring between 90° and 180°.

Straight Angle

An angle measuring exactly 180°.

Complementary Angles

Two angles whose measures sum to 90°.

Supplementary Angles

Two angles whose measures sum to 180°.

Transversal

A line intersecting two or more coplanar lines.

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Midpoint Formula

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Slope Formula

m = (y₂ - y₁)/(x₂ - x₁)

Slope-Intercept Form

y = mx + b

Point-Slope Form

y - y₁ = m(x - x₁)

Parallel Lines Slope

m₁ = m₂ (Slopes are equal)

Perpendicular Lines Slope

m₁ · m₂ = -1 (Opposite reciprocals)

Congruent

Figures with identical shape and size.

Isosceles Triangle

Triangle with at least two congruent sides.

Equilateral Triangle

Triangle with three congruent sides.

Scalene Triangle

Triangle with no congruent sides.

Median

Segment from a vertex to the opposite midpoint.

Centroid

Point where three medians of a triangle intersect.

Altitude

Perpendicular segment from a vertex to the opposite side.

Orthocenter

Point where three altitudes of a triangle intersect.

Perpendicular Bisector

Line perpendicular to a segment at its midpoint.

Circumcenter

Point where three perpendicular bisectors intersect.

Angle Bisector

Ray dividing an angle into two equal angles.

Incenter

Point where three angle bisectors intersect.

Midsegment

Segment connecting midpoints of two triangle sides.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent.

Triangle Inequality Theorem

The sum of two shorter sides must exceed the longest side (a + b > c).

Triangle Midsegment Theorem

Midsegment = ½(Parallel Base)

Similar Figures

Figures with congruent angles and proportional side lengths.

Scale Factor

Ratio of corresponding linear measurements of two shapes.

Proportion

An equation stating that two numerical ratios are equal.

Sine Ratio

sin(θ) = Opposite / Hypotenuse

Cosine Ratio

cos(θ) = Adjacent / Hypotenuse

Tangent Ratio

tan(θ) = Opposite / Adjacent

45-45-90 Special Triangle

Legs = x, Hypotenuse = x√2

30-60-90 Special Triangle

Short Leg = x, Long Leg = x√3, Hypotenuse = 2x

Parallelogram

Quadrilateral with two pairs of parallel opposite sides.

Rhombus

Parallelogram featuring four congruent sides.

Rectangle

Parallelogram featuring four right angles.

Square

Parallelogram featuring four congruent sides and four right angles.

Trapezoid

Quadrilateral featuring exactly one pair of parallel sides.

Kite

Quadrilateral with two pairs of consecutive congruent sides.

Circle

Set of all coplanar points equidistant from a center.

Radius

Segment connecting circle center to any outer point.

Diameter

Chord passing directly through the circle center point.

Chord

Segment whose endpoints both lie on a circle.

Tangent Line

Line intersecting a circle at exactly one point.

Secant Line

Line intersecting a circle at two distinct points.

Central Angle

Angle whose vertex is the circle center point.

Inscribed Angle

Angle whose vertex lies directly on the circle.

Polygon Exterior Angles Sum

Always 360°

Standard Circle Equation

(x - h)² + (y - k)² = r² with center (h, k).

Surface Area

Total area covering all external faces of a solid.

Lateral Area

Surface area of a solid excluding its bases.

Volume

Amount of three-dimensional space a solid object occupies.