Mathematics 9 Geometry Review Flashcards

A set of vocabulary flashcards covering quadrilateral definitions, parallelogram properties, geometric formulas, and triangle congruence theorems from Mathematics 9.

Consecutive Angles of a Parallelogram

Angles that share a common side in a parallelogram; they are always supplementary, meaning their sum equals $180^\bullet$.

Perimeter of a Rhombus

The total distance around a rhombus, calculated by multiplying the length of one side by four; for example, a rhombus with a perimeter of $72\,\text{cm}$ has side lengths of $18\,\text{cm}$.

Area Formula of a Rhombus

The area formula given by $A = \frac{1}{2}d_1 d_2$, where $d_1$ and $d_2$ represent the lengths of the two diagonals.

Perimeter of a Parallelogram

The total distance around a parallelogram, calculated using the formula $P = 2(a + b)$, where $a$ and $b$ are the lengths of adjacent sides.

Rectangle

A specific quadrilateral classified as a parallelogram with four right angles, whose adjacent sides are not required to be congruent.

Square

A quadrilateral defined by having four congruent sides and four right angles, making it simultaneously a rectangle and a rhombus.

Diagonals of a Parallelogram

Line segments connecting opposite vertices of a parallelogram that always bisect each other at their point of intersection.

Diagonals of a Rectangle

Line segments connecting opposite vertices of a rectangle that are always congruent; their length can be calculated using the Pythagorean theorem ($a^2 + b^2 = c^2$) on the length and width.

Perpendicular Height of a Parallelogram

The altitude segment perpendicular to the base used to calculate area (\text{Area} = \text{base} \times \text{height}); it cannot be assumed to equal the slanted adjacent side length.

ASA Congruence Theorem

A triangle congruence theorem that applies when two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

CPCTC

An acronym for 'Corresponding Parts of Congruent Triangles are Congruent,' which justifies that corresponding sides or angles are equal after two triangles are proven congruent.

Proof Plan for Opposite Sides of a Parallelogram

A geometric proof method that shows two angle pairs congruent from parallel lines, uses a diagonal as a common side to apply ASA, and concludes that opposite sides are congruent using CPCTC.

SSS Congruence Theorem for Rhombus Diagonals

The most direct congruence theorem used when comparing triangles $ABC$ and $ADC$ to prove that diagonal $AC$ of rhombus $ABCD$ bisects $\angle A$.

Diagonals Bisecting Each Other Condition

A geometric property that proves a quadrilateral is a parallelogram, but alone is insufficient to prove that it is a rectangle.