Geometry Lecture Notes Review

Comprehensive vocabulary flashcards covering basic geometry definitions, reasoning, parallel lines, triangle congruence, triangle relationships, quadrilaterals, and similarity.

Point

An exact location.

Line

Extends forever in both directions.

Plane

A flat surface extending forever.

Segment

Part of a line with two endpoints.

Ray

Starts at one endpoint and extends forever.

Segment Addition Postulate

If $B$ is between $A$ and $C$, then $AB + BC = AC$.

Angle Addition Postulate

If $D$ is inside $\angle ABC$, then $\angle ABD + \angle DBC = \angle ABC$.

Midpoint

Divides a segment into two congruent segments.

Segment Bisector

Passes through the midpoint of a segment.

Angle Bisector

Divides an angle into two congruent angles.

Law of Detachment

If $p \rightarrow q$ and $p$ is true, then $q$ is true.

Law of Syllogism

If $p \rightarrow q$ and $q \rightarrow r$, then $p \rightarrow r$.

Vertical Angles Theorem

Vertical angles are congruent.

Linear Pair Theorem

Linear pair angles are supplementary.

Congruent Supplements Theorem

Supplements of the same angle are congruent.

Congruent Complements Theorem

Complements of the same angle are congruent.

Triangle Congruence Theorems

Rules stating that triangles are congruent under the conditions: SSS, SAS, ASA, AAS, or HL (right triangles only).

CPCTC

Corresponding Parts of Congruent Triangles are Congruent.

Isosceles Triangle Theorem

If two sides are congruent, then the opposite angles are congruent.

Converse Isosceles Triangle Theorem

If two angles are congruent, then the opposite sides are congruent.

Triangle Sum Theorem

The interior angles of a triangle add to $180^\circ$.

Exterior Angle Theorem

An exterior angle equals the sum of the two remote interior angles.

Triangle Inequality Theorem

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

Perpendicular Bisector Theorem

A point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.

Angle Bisector Theorem

A point on an angle bisector is equidistant from the sides of the angle.

Circumcenter

The intersection of perpendicular bisectors; equidistant from the vertices.

Incenter

The intersection of angle bisectors; equidistant from the sides.

Centroid

The intersection of medians; divides each median in a $2:1$ ratio.

Orthocenter

The intersection of altitudes.

Median

Connects a vertex to the midpoint of the opposite side.

Altitude

Connects a vertex perpendicular to the opposite side.

Triangle Midsegment Theorem

A midsegment is parallel to the third side and half the length of the third side.

Hinge Theorem (SAS Inequality)

If two triangles have two congruent sides, the triangle with the larger included angle has the longer third side.

Interior Angle Sum

For a polygon with $n$ sides, the sum is $(n-2) \times 180^\circ$.

Exterior Angle Sum

Always $360^\circ$ for any polygon.

Rectangle

A parallelogram with four right angles and congruent diagonals.

Rhombus

A parallelogram with four congruent sides and perpendicular diagonals.

Square

A quadrilateral that is both a rectangle and a rhombus, with four congruent sides and four right angles.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Isosceles Trapezoid

A trapezoid with congruent legs, congruent base angles, and congruent diagonals.

Trapezoid Midsegment Formula

$$\text{Midsegment} = \frac{b_1 + b_2}{2}$$

Kite

A quadrilateral with two distinct pairs of adjacent congruent sides and perpendicular diagonals.

Ratio

A comparison of two quantities by division.

Proportion

An equation stating that two ratios are equal.

Geometric Mean

The geometric mean of two numbers $a$ and $b$ is $\sqrt{ab}$.