Basics of Geometry Vocabulary

A complete set of vocabulary flashcards based on Big Ideas Geometry Chapter 1 Study Guide covering definitions, postulates, and geometric formulas.

Undefined Terms

Point, line, and plane; the fundamental building blocks of geometry that cannot be defined using other figures.

Distance

The absolute value of the difference of the coordinates of points $A$ and $B$.

Midpoint

The point on a segment that divides the segment into two congruent segments.

Congruent ($\cong$)

The description of two geometric figures which have the same size and shape.

Segment Bisector

Anything that divides a segment into two equal lengths.

Angle Bisector

A segment, line, or ray through the vertex of an angle that divides the angle into two equal measures.

Complementary Angles

Two angles whose measures have a sum of $90^\circ$.

Supplementary Angles

Two angles whose measures have a sum of $180^\circ$.

Adjacent Angles

Two coplanar angles that share a common vertex and side, but have no common interior points.

Vertical Angles

Two nonadjacent angles formed by two intersecting lines.

Linear Pair

Two adjacent angles when their non-common sides are opposite rays.

Polygon

A closed plane figure formed by three or more line segments.

Convex Polygon

A polygon in which no diagonals fall outside the polygon.

Concave Polygon

A polygon in which at least one diagonal falls outside the polygon.

Ruler Postulate

The postulate stating that the points on a line can be matched one to one with the real numbers, where the real number corresponding to a point is its coordinate.

Segment Addition Postulate

If $B$ is between $A$ and $C$, then $m\overline{AB} + m\overline{BC} = m\overline{AC}$.

Protractor Postulate

The rays of the form $\overrightarrow{OA}$ can be matched one to one with the real numbers from $0$ to $180$.

Angle Addition Postulate

If $S$ is in the interior of $\angle PQR$, then $m\angle PQS + m\angle SQR = m\angle PQR$.

Distance Formula

$$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$

Midpoint Formula

$$M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$

Rectangle Formulas

Perimeter: $P = 2l + 2w$; Area: $A = l \cdot w$

Triangle Formulas

Perimeter: $P = a + b + c$; Area: $A = \frac{1}{2}bh$

Types of Polygons

Named polygons based on side count: triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon, and n-gon.