Geometry Study Guide

Flashcards covering key vocabulary and concepts for Geometry, based on the study guide for the 1st semester final exam.

Point

An exact location in space with no size or dimension.

Line

A straight one-dimensional figure that has no thickness and extends infinitely in both directions.

Plane

A flat two-dimensional surface that extends infinitely in all directions.

Collinear

Points that lie on the same straight line.

Coplanar

Points that lie in the same plane.

Midpoint Formula

The formula used to find the midpoint between two points, given as ((x1+x2)/2, (y1+y2)/2).

Distance Formula

The formula used to calculate the distance between two points in a plane, defined as √((x2-x1)² + (y2-y1)²).

Right Angle

An angle that measures 90 degrees.

Obtuse Angle

An angle that measures more than 90 degrees but less than 180 degrees.

Acute Angle

An angle that measures less than 90 degrees.

Adjacent Angles

Two angles that share a common side and a vertex but do not overlap.

Linear Pair

A pair of adjacent angles formed when two lines intersect.

Complementary Angles

Two angles whose sum is 90 degrees.

Supplementary Angles

Two angles whose sum is 180 degrees.

Segment Bisector

A point, line, or plane that divides a segment into two equal parts.

Angle Bisector

A ray that divides an angle into two equal angles.

Triangle

A polygon with three sides.

Quadrilateral

A polygon with four sides.

Pentagon

A polygon with five sides.

Regular Polygon

A polygon with all sides and angles equal.

Irregular Polygon

A polygon with sides and angles that are not all equal.

Convex Polygon

A polygon where all interior angles are less than 180 degrees.

Concave Polygon

A polygon that has at least one interior angle greater than 180 degrees.

If-Then Statement

A statement of the form 'If P, then Q' where P is a hypothesis and Q is a conclusion.

Converse

The statement formed by reversing the hypothesis and conclusion of a conditional statement.

Inverse

The statement formed by negating both the hypothesis and conclusion of a conditional statement.

Contrapositive

The statement formed by reversing and negating both the hypothesis and conclusion of a conditional statement.

Symmetric Property

If a = b, then b = a.

Reflexive Property

For any quantity a, a = a.

Transitive Property

If a = b and b = c, then a = c.

Slope of a Line

A measure of the steepness of a line, calculated as rise/run.

Parallel Lines

Lines that never intersect and are always the same distance apart.

Perpendicular Lines

Lines that intersect at a right angle.

Point-Slope Form of a Line

An equation of the form y - y1 = m(x - x1) where (x1, y1) is a point on the line and m is the slope.

Angle Sum Theorem

The sum of the interior angles of a triangle is always 180 degrees.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Scalene Triangle

A triangle with all sides of different lengths.

Equilateral Triangle

A triangle with all sides of equal length.

Isosceles Triangle

A triangle with at least two sides of equal length.

Congruent Triangles

Triangles that are identical in shape and size, can be proven using SSS, SAS, AAS, or ASA.

Perpendicular Bisector

A line that divides a segment into two equal parts at a right angle.

Median of a Triangle

A line segment from a vertex to the midpoint of the opposite side.

Altitude of a Triangle

A perpendicular segment from a vertex to the line containing the opposite side.

Angle Relationship in Triangles

In a triangle, the largest angle corresponds to the longest side and vice versa.

Triangle Inequality Theorem

For any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Parallelogram Properties

Opposite sides are equal and parallel, opposite angles are equal.

Rectangle Properties

A parallelogram with four right angles.

Rhombus Properties

A parallelogram with all sides equal; diagonals bisect at right angles.

Square Properties

A rectangle with all sides equal.

Trapezoid Properties

A quadrilateral with at least one pair of parallel sides.

Median of a Trapezoid

The segment that connects the midpoints of the non-parallel sides.

Kite Properties

A quadrilateral with two distinct pairs of adjacent sides that are equal.