Geometry Chapter 6 Flashcards

Questions and Answers

What is the definition of a rectangle?

A parallelogram with 4 right angles.

What is the definition of a rhombus?

A parallelogram with all sides congruent.

What is the definition of a square?

A parallelogram with 4 right angles and all sides congruent.

If a parallelogram is a rhombus, what can be said about its diagonals?

The diagonals are perpendicular to each other. Signup and view all the answers

If a parallelogram is a rhombus, what do the diagonals bisect?

Each diagonal bisects a pair of opposite angles of the rhombus. Signup and view all the answers

What is true about the diagonals of a rectangle?

They are congruent. Signup and view all the answers

Name 2 special properties of rhombuses.

Diagonals are perpendicular; each diagonal bisects a pair of opposite angles. Signup and view all the answers

What are 2 ways to prove a parallelogram is a rectangle?

If the diagonals of a parallelogram are congruent, then it's a rectangle; if a parallelogram has one right angle, then it's a rectangle. Signup and view all the answers

What are 2 ways to prove a parallelogram is a rhombus?

If the diagonals of a parallelogram are perpendicular, then it's a rhombus; if one diagonal bisects a pair of opposite angles, then it is a rhombus. Signup and view all the answers

What is 1 way to prove a rectangle is a square?

If 2 consecutive sides of a rectangle are congruent, then it's a square. Signup and view all the answers

What is 1 way to prove a rhombus is a square?

If a rhombus has one right angle, then it is a square. Signup and view all the answers

What is the definition of a trapezoid?

A quadrilateral with exactly one pair of opposite sides parallel. Signup and view all the answers

What is the definition of an isosceles trapezoid?

A trapezoid with legs that are congruent. Signup and view all the answers

What can be said about the base angles of an isosceles trapezoid?

The base angles are congruent. Signup and view all the answers

If a quadrilateral is an isosceles trapezoid, what can be said about its diagonals?

The diagonals are congruent. Signup and view all the answers

What is the definition of a kite?

A quadrilateral with exactly 2 pairs of congruent consecutive sides and no opposite sides congruent. Signup and view all the answers

What can be said about the diagonals of a kite?

The diagonals are perpendicular. Signup and view all the answers

What happens to the vertex angles of a kite?

They are bisected by the diagonal. Signup and view all the answers

What is the definition of a polygon?

A closed figure formed by coplanar segments. Signup and view all the answers

What does only ONE set of sides on a quadrilateral have to be in order for it to be a parallelogram?

Congruent and parallel. Signup and view all the answers

If BOTH PAIRS of opposite sides of a quadrilateral are __________, then the quadrilateral is a parallelogram.

congruent or parallel. Signup and view all the answers

What is the polygon angle sum theory?

(N-2)180 = sum interior angle. Signup and view all the answers

What is the definition of a parallelogram?

A quadrilateral with both pairs of opposite sides parallel. Signup and view all the answers

If a quadrilateral is a parallelogram, then the opposite angles are __________.

congruent. Signup and view all the answers

If the diagonals of a quadrilateral __________, then the quadrilateral is a parallelogram.

bisect. Signup and view all the answers

If the angles in a quadrilateral are __________ with their consecutive angles, then the quadrilateral is a parallelogram.

supplementary. Signup and view all the answers

What is the polygon exterior angle sum theory?

The sum of the exterior angles is equal to 360. Signup and view all the answers

The measure of each interior angle of a regular polygon is __________.

(N-2)180 / N. Signup and view all the answers

The measure of the interior angle is __________ to the measure of the exterior angle.

supplementary. Signup and view all the answers

What is a convex polygon?

A polygon where no line containing a side of the polygon contains a point of the interior of the polygon. Signup and view all the answers

What are three ways to prove a polygon to a parallelogram involving sides?

<ol> <li>Both pairs of opposite sides are parallel; 2) Both pairs of opposite sides are congruent; 3) One set of opposite sides is parallel and congruent.</li> </ol> Signup and view all the answers

Study Notes

Rectangle

A parallelogram characterized by having four right angles.

Rhombus

A parallelogram where all sides are congruent, often described as a “squished square.”

Square

A special type of parallelogram that has four right angles and all sides congruent. It can be viewed as a rectangle or a rhombus with equal sides.

Diagonals of a Rhombus

If a parallelogram is a rhombus, its diagonals are perpendicular to each other.
Each diagonal bisects a pair of opposite angles.

Diagonals of a Rectangle

The diagonals in a rectangle are congruent.

Properties of Rhombuses

Two key properties: diagonals are perpendicular and each diagonal bisects a pair of opposite angles.

Proving a Rectangle

A parallelogram is a rectangle if its diagonals are congruent, or if it has one right angle.

Proving a Rhombus

A parallelogram is a rhombus if its diagonals are perpendicular, if one diagonal bisects a pair of opposite angles, or if two consecutive sides are congruent.

Proving a Rectangle is a Square

A rectangle becomes a square if two consecutive sides are congruent.

Proving a Rhombus is a Square

A rhombus is identified as a square if it contains at least one right angle.

Trapezoid

Defined as a quadrilateral with exactly one pair of parallel opposite sides.

Isosceles Trapezoid

A trapezoid with legs that are congruent, resulting in equal base angles and congruent diagonals.

Theorems of Isosceles Trapezoid

Base angles are congruent, and the diagonals are congruent.

Kite

A quadrilateral with exactly two pairs of congruent consecutive sides and no opposite sides congruent.

Properties of Kites

Diagonals are perpendicular.
Vertex angles are bisected by the diagonal.
Non-vertex angles are congruent.

Polygon

A closed figure with coplanar segments that intersect only at endpoints; no two segments may share a common endpoint in a linear fashion.

Parallelogram Conditions

A quadrilateral can be classified as a parallelogram if either one set of opposite sides is both congruent and parallel or if both pairs of opposite sides are congruent or parallel.

Polygon Angle Sum Theory

The sum of the interior angles of a polygon can be calculated using the formula (N-2) × 180, where N is the number of sides.

Parallelogram Definition

A quadrilateral having both pairs of opposite sides parallel.

Congruent Angles in Parallelograms

In a parallelogram, opposite angles are congruent.

Properties of Diagonals in Parallelograms

If the diagonals bisect each other, the quadrilateral is a parallelogram.

Supplementary Angles in Parallelograms

If the consecutive angles of a quadrilateral are supplementary, then it is a parallelogram.

Parallel Lines and Transversals

If three or more parallel lines cut off congruent segments on one transversal, they will cut off congruent segments on any transversal.

Polygon Exterior Angle Sum Theory

The sum of the exterior angles of any polygon is always equal to 360 degrees.

Regular Polygon Interior Angle Measure

The measure of each interior angle in a regular polygon is calculated using (N-2) × 180 / N.

Relation Between Interior and Exterior Angles

Each interior angle is supplementary to its corresponding exterior angle.

Convex Polygon

A polygon where no line containing a side of the polygon contains a point in the interior.

Methods of Proving a Quadrilateral is a Parallelogram

Three methods involving sides: both pairs of opposite sides are parallel; both pairs of opposite sides are congruent; one set of opposite sides is both parallel and congruent.

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Description

This quiz features flashcards covering key definitions in Chapter 6 of Geometry. From understanding rectangles and rhombuses to the unique properties of squares, this study guide is perfect for mastering the concepts of parallelograms. Test your knowledge and enhance your geometry skills with these essential terms.