Geometry and Algebra Lecture Notes Review

Vocabulary practice flashcards covering fundamental geometry quadrilateral properties, angle relationships, coordinate geometry line equations, and basic algebraic function evaluations.

Evaluation of $y = 3x + 2$ at $x = 4$

$$y = 14$$

Perimeter of a Parallelogram Formula

$P = 2(a + b)$; for sides $7\,\text{cm}$ and $10\,\text{cm}$, the perimeter is $34\,\text{cm}$.

Parallelogram (Diagonal Property)

A quadrilateral whose diagonals bisect each other, but are not necessarily equal.

Area of a Rectangle Formula

$A = l \times w$; for length $12\,\text{cm}$ and width $5\,\text{cm}$, the area is $60\,\text{cm}^2$.

Square (Diagonal Property)

A quadrilateral whose diagonals bisect each other at right angles and are equal.

Slope of a Line through $(0,6)$ and $(3,0)$

$$-2$$

Opposite Sides of a Parallelogram

Opposite sides in a parallelogram are equal and parallel.

Rectangle (Diagonal Property)

A quadrilateral whose diagonals are equal and bisect each other.

Rectangle Definition

A quadrilateral with equal diagonals and four right angles.

Linear Cellphone Plan Equation

$y = 8x + 600$, representing a monthly charge of $\text{P}600$ plus $8$ per text.

Consecutive Angles of a Parallelogram

Consecutive angles are supplementary; if one angle is $80^\circ$, the adjacent angle is $100^\circ$.

Slope Interpretation in $y = 300x$

In the context of concert tickets, the coefficient $300$ represents the cost per ticket.

Same-Side Interior Angles

A pair of interior angles on the same side of a transversal intersecting parallel lines that are always supplementary.

Square Definition

A quadrilateral with four equal sides and four right angles.

Alternate Interior Angles

Congruent angles formed on opposite sides of a transversal cutting parallel lines; if one angle is $75^\circ$, the alternate interior angle is $75^\circ$.

Interior Angle of a Rectangle

Each interior angle of a rectangle measures $90^\circ$.

Perimeter of a Square Formula

$P = 4s$; for a square with side length $9\,\text{cm}$, the perimeter is $36\,\text{cm}$.

Zero of the Function $f(x) = 3x - 9$

$$x = 3$$

Condition for Parallel Lines

Two lines are parallel if and only if they have the same slope.

Slope Condition for Perpendicular Lines

The product of the slopes of two perpendicular lines must equal $-1$; lines with slopes $3$ and $-3$ are not perpendicular.

Slope of a Line through $(1,3)$ and $(5,1)$

$$-\frac{1}{2}$$

Square-to-Rectangle Classification

A square is always a rectangle because it has four right angles and opposite sides equal.

Rectangle Diagonals Orthogonality

The claim that diagonals of a rectangle are perpendicular is incorrect.

Negative Slope Visual Representation

A graph showing a line that falls gently to the right.

Complementary Angles

Two angles whose sum is $90^\circ$ (e.g., $35^\circ$ and $55^\circ$).

Perpendicular Line Equations Example

Equations such as $y = 4x$ and $y = -\frac{1}{4}x$, where the product of their slopes is $-1$.

Non-Linear Relationship Example

The area of a circle as its radius increases ($A = \pi r^2$).

Linear Function Graph

A relationship represented visually by a straight line graph.

Diagonal of a Square Formula

For a square with side length $8\,\text{cm}$, the diagonal length is $8\sqrt{2}\,\text{cm}$.

Linear Cost Function Model

$y = 25x + 150$, modeling a company charging a fixed fee of $\$150$ plus $\$25$ per hour.

Trapezoid Definition

A quadrilateral with exactly one pair of parallel sides.

Area of a Parallelogram Formula

$A = b \times h$; for base $15\,\text{cm}$ and height $6\,\text{cm}$, the area is $90\,\text{cm}^2$.

Linear Equation Solving Correction ($3x + 6 = 0$)

Solving $3x + 6 = 0$ gives $3x = -6$, leading to $x = -2$ (not $x = -6$).

Horizontal Line Slope

A line with a slope of $0$ is represented visually as a horizontal line.

Equation of Line through $(0,1)$ and $(3,10)$

$$y = 3x + 1$$

Corresponding Angles

Congruent angles in matching relative positions when a transversal cuts parallel lines.

Area of a Trapezoid Formula

$$A = \frac{b_1 + b_2}{2}h$$

Product of Slopes for Perpendicular Lines

$$-1$$

Rhombus (Diagonal Property)

A quadrilateral whose diagonals are unequal in length and perpendicular to each other.

Parallelogram Definition

A quadrilateral with opposite sides parallel.

Equation of Line with Slope $3$ through $(0,6)$

$$y = 3x + 6$$

Perpendicular Lines Angle Measure

The angle formed by two perpendicular lines is $90^\circ$.