Podcast
Questions and Answers
What is the definition of a rectangle?
What is the definition of a rectangle?
A parallelogram with 4 right angles.
What is the definition of a rhombus?
What is the definition of a rhombus?
A parallelogram with all sides congruent.
What is the definition of a square?
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?
If a parallelogram is a rhombus, what can be said about its diagonals?
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If a parallelogram is a rhombus, what do the diagonals bisect?
If a parallelogram is a rhombus, what do the diagonals bisect?
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What is true about the diagonals of a rectangle?
What is true about the diagonals of a rectangle?
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Name 2 special properties of rhombuses.
Name 2 special properties of rhombuses.
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What are 2 ways to prove a parallelogram is a rectangle?
What are 2 ways to prove a parallelogram is a rectangle?
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What are 2 ways to prove a parallelogram is a rhombus?
What are 2 ways to prove a parallelogram is a rhombus?
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What is 1 way to prove a rectangle is a square?
What is 1 way to prove a rectangle is a square?
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What is 1 way to prove a rhombus is a square?
What is 1 way to prove a rhombus is a square?
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What is the definition of a trapezoid?
What is the definition of a trapezoid?
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What is the definition of an isosceles trapezoid?
What is the definition of an isosceles trapezoid?
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What can be said about the base angles of an isosceles trapezoid?
What can be said about the base angles of an isosceles trapezoid?
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If a quadrilateral is an isosceles trapezoid, what can be said about its diagonals?
If a quadrilateral is an isosceles trapezoid, what can be said about its diagonals?
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What is the definition of a kite?
What is the definition of a kite?
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What can be said about the diagonals of a kite?
What can be said about the diagonals of a kite?
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What happens to the vertex angles of a kite?
What happens to the vertex angles of a kite?
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What is the definition of a polygon?
What is the definition of a polygon?
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What does only ONE set of sides on a quadrilateral have to be in order for it to be a parallelogram?
What does only ONE set of sides on a quadrilateral have to be in order for it to be a parallelogram?
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If BOTH PAIRS of opposite sides of a quadrilateral are __________, then the quadrilateral is a parallelogram.
If BOTH PAIRS of opposite sides of a quadrilateral are __________, then the quadrilateral is a parallelogram.
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What is the polygon angle sum theory?
What is the polygon angle sum theory?
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What is the definition of a parallelogram?
What is the definition of a parallelogram?
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If a quadrilateral is a parallelogram, then the opposite angles are __________.
If a quadrilateral is a parallelogram, then the opposite angles are __________.
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If the diagonals of a quadrilateral __________, then the quadrilateral is a parallelogram.
If the diagonals of a quadrilateral __________, then the quadrilateral is a parallelogram.
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If the angles in a quadrilateral are __________ with their consecutive angles, then the quadrilateral is a parallelogram.
If the angles in a quadrilateral are __________ with their consecutive angles, then the quadrilateral is a parallelogram.
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What is the polygon exterior angle sum theory?
What is the polygon exterior angle sum theory?
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The measure of each interior angle of a regular polygon is __________.
The measure of each interior angle of a regular polygon is __________.
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The measure of the interior angle is __________ to the measure of the exterior angle.
The measure of the interior angle is __________ to the measure of the exterior angle.
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What is a convex polygon?
What is a convex polygon?
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What are three ways to prove a polygon to a parallelogram involving sides?
What are three ways to prove a polygon to a parallelogram involving sides?
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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.
