Grade 9 Mathematics: Quadrilaterals, Linear Functions, and Line Relationships

Vocabulary review flashcards covering properties and definitions of quadrilaterals, parallelograms, linear functions, line relationships, and coplanar geometry.

Parallel Lines

Lines in the same plane that are always equidistant (the same distance apart), never meet, and have equal slopes.

Perpendicular Lines

Two lines that intersect each other to form a $90^\text{o}$ angle (right angle) and have slopes that are negative reciprocals.

Polygon

A closed plane figure formed by connecting three or more segments at their endpoints.

Adjacent Sides of a Polygon

Two sides of a polygon that share a common endpoint.

Quadrilateral

A closed plane figure consisting of four line segments or sides.

Convex Quadrilateral

A quadrilateral in which all four interior angles measure less than $180^\text{o}$ and both diagonals lie entirely inside the figure.

Concave Quadrilateral

A quadrilateral in which one interior angle measures greater than $180^\text{o}$ and one diagonal lies outside the figure.

Sum of Interior Angles of a Quadrilateral

The total sum of the interior angle measures in any quadrilateral, which is always equal to $360^\text{o}$.

Parallelogram

A quadrilateral with two pairs of opposite sides parallel and congruent.

Rectangle

A parallelogram with four right angles and congruent diagonals.

Rhombus

A parallelogram with four congruent sides, perpendicular diagonals, and diagonals that bisect opposite angles.

Square

A parallelogram with four congruent sides and four right angles, combining all properties of both a rectangle and a rhombus.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Isosceles Trapezoid

A trapezoid whose non-parallel sides (legs) are congruent.

Kite

A quadrilateral with two distinct pairs of adjacent, congruent sides.

Trapezium

A quadrilateral that has no parallel sides.

Linear Function

A function represented by the equation $y = mx + b$, where $m$ and $b$ are constants, $x$ is the independent variable, and $y$ is the dependent variable.

Coplanar Lines

Lines that lie on the exact same plane.

Non-coplanar Lines

Lines that do not lie on the same plane and do not intersect.

Slope Condition for Parallelism

The condition stating that two distinct nonvertical lines are parallel if and only if their slopes are equal ($m_1 = m_2$).

Slope Condition for Perpendicularity

The condition stating that two nonvertical lines are perpendicular if and only if their slopes are negative reciprocals ($m_1 \times m_2 = -1$).

Standard-Form Perpendicular Test

An algebraic test confirming two lines in standard form are perpendicular if $A_1 A_2 + B_1 B_2 = 0$.