Geometry Unit 4: Triangles, Polygons, and Quadrilateral Properties

Vocabulary review flashcards covering definitions, properties, angle sum formulas, and side length theorems for triangles, quadrilaterals, and polygons.

Scalene Triangle

A triangle with no equal sides.

Isosceles Triangle

A triangle with $2$ equal (congruent) sides and $2$ congruent base angles.

Equilateral Triangle

A triangle in which all sides are equal.

Acute Triangle

A triangle that contains $3$ acute angles.

Right Triangle

A triangle that contains exactly $1$ right angle.

Obtuse Triangle

A triangle that contains exactly $1$ obtuse angle.

Triangle Interior Angle Sum

The theorem stating that the sum of all interior angles of a triangle is equal to $180^\circ$.

Congruent ($\cong$)

Objects that are exactly the same size, equal ($=$), and have the same shape.

Equiangular Triangle

A triangle in which all $3$ interior angles are congruent ($\cong$), with each measuring $\frac{180^\circ}{3} = 60^\circ$.

Quadrilateral

A $4$-sided geometric figure whose interior angles sum to $360^\circ$.

Trapezoid

A quadrilateral that has $1$ pair of opposite parallel ($\parallel$) sides and $1$ pair of opposite non-parallel sides.

Parallelogram

A quadrilateral characterized by $2$ pairs of opposite parallel ($\parallel$) sides, $2$ pairs of opposite congruent ($\cong$) sides, opposite angles that are congruent, and consecutive angles that are supplementary (sum to $180^\circ$).

Rectangle

A parallelogram with $4$ right angles that retains all properties of a parallelogram.

Rhombus

A parallelogram with $4$ congruent ($\cong$) sides that retains all properties of a parallelogram.

Square

A quadrilateral that possesses all properties of a parallelogram, $4$ right angles, and $4$ congruent ($\cong$) sides.

Polygon Interior Angle Sum Formula

The mathematical formula $180^\circ \times (n - 2)$, used to determine the sum of all interior angles of an $n$-sided polygon.

Hexagon Interior Angle Sum

The total degree measure of the interior angles of a $6$-sided polygon, evaluated as $180^\circ \times (6 - 2) = 180^\circ \times 4 = 720^\circ$, where each angle in a regular hexagon equals $120^\circ$.

Heptagon

A polygon with $7$ sides, whose interior angle sum is computed as $180^\circ \times (7 - 2)$.

Longest Side Angle Relationship

The property in a triangle where the longest side is always positioned opposite the largest interior angle.

Shortest Side Angle Relationship

The property in a triangle where the shortest side is always positioned opposite the smallest interior angle.

Triangle Inequality Theorem

The rule stating that the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.

Third Side Range Rule

The principle stating that the length of the third side of a triangle must be strictly less than the sum and strictly greater than the difference of the lengths of the other two sides.