Quadrilaterals and Their Properties Quiz

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

If the diagonals of a parallelogram are equal, then the parallelogram is a _______.

rectangle

The diagonals of a square are ____ and ____ to each other.

equal, perpendicular

If a diagonal of a parallelogram bisects one of its angles, then the parallelogram is a ______.

rhombus

A rectangle in which each diagonal divides it into two congruent equilateral triangles is a ______.

<p>square</p> Signup and view all the answers

A quadrilateral whose all sides are equal and all angles measures $90^o$ is a ______.

<p>square</p> Signup and view all the answers

The diagonals of a rectangle ______ each other.

<p>bisect</p> Signup and view all the answers

The diagonals of a rhombus are ______ to each other.

<p>perpendicular</p> Signup and view all the answers

Opposite angles of a parallelogram are always equal.

<p>True (A)</p> Signup and view all the answers

All squares are rectangles, but not all rectangles are squares.

<p>True (A)</p> Signup and view all the answers

The diagonals of a rhombus bisect each other at right angles.

<p>True (A)</p> Signup and view all the answers

A parallelogram is a quadrilateral with opposite sides parallel but not equal.

<p>False (B)</p> Signup and view all the answers

All quadrilaterals are parallelograms.

<p>False (B)</p> Signup and view all the answers

The diagonals of a rhombus are not equal in length.

<p>True (A)</p> Signup and view all the answers

Match the following quadrilaterals with their defining property:

<p>Square = All sides are equal, and all angles are right angles. Rectangle = Opposite sides are parallel and equal, and all angles are right angles. Parallelogram = Opposite sides are parallel and equal. Rhombus = All sides are equal, and diagonals are perpendicular bisectors.</p> Signup and view all the answers

Flashcards

Parallelogram Definition

A quadrilateral with opposite sides parallel and equal.

Diagonal Equality in Parallelograms

In a parallelogram, if the diagonals are equal, it is a rectangle.

Right Angles in Rectangles

A rectangle has four right angles (90° each).

Angle Sum in Quadrilaterals

The sum of interior angles in a quadrilateral is 360°.

Signup and view all the flashcards

Congruent Triangles

Triangles that are identical in size and shape; three parts must be equal.

Signup and view all the flashcards

SSS Congruence Rule

If three sides of one triangle are equal to three sides of another, they are congruent.

Signup and view all the flashcards

SAS Congruence Rule

If two sides and the included angle of one triangle equal two sides and the included angle of another triangle, they are congruent.

Signup and view all the flashcards

ASA Congruence Rule

If two angles and the intervening side of one triangle are equal to two angles and the corresponding side of another, they are congruent.

Signup and view all the flashcards

Vertical Angles

Angles opposite each other when two lines intersect; they are always equal.

Signup and view all the flashcards

Complementary Angles

Two angles whose sum is 90°.

Signup and view all the flashcards

Supplementary Angles

Two angles whose sum is 180°.

Signup and view all the flashcards

Properties of Squares

A square has all sides equal, four right angles, and diagonals that bisect each other at 90°.

Signup and view all the flashcards

Diagonals in Squares

The diagonals of a square are equal and bisect each other at right angles.

Signup and view all the flashcards

Angle Bisector

A line that divides an angle into two equal parts.

Signup and view all the flashcards

Consequences of Right Angles

A parallelogram with one right angle is a rectangle.

Signup and view all the flashcards

Equilateral Quadrilateral

A quadrilateral with all four sides equal is a rhombus.

Signup and view all the flashcards

Transversal Lines

A line that intersects two or more lines at different points.

Signup and view all the flashcards

Interior Angles

Angles formed inside a polygon by its sides.

Signup and view all the flashcards

Angle Relationships

Certain angles can be equal, supplementary, or complementary based on their position.

Signup and view all the flashcards

Quadrilateral Types

Common quadrilaterals include squares, rectangles, rhombuses, and trapezoids.

Signup and view all the flashcards

Circle Theorem

A line from the center of a circle to any point on the circle is a radius.

Signup and view all the flashcards

Perpendicular Bisectors

A line that divides a segment into two equal parts at a right angle.

Signup and view all the flashcards

Alternate Interior Angles

Angles on opposite sides of a transversal that lie inside the two lines.

Signup and view all the flashcards

Transitive Property of Equality

If a = b and b = c, then a = c.

Signup and view all the flashcards

Equidistant

Points that are the same distance from two other points.

Signup and view all the flashcards

Angle Complementation

Finding a complementary angle to reach 90°.

Signup and view all the flashcards

Area of a Parallelogram

Base times height; A = b × h.

Signup and view all the flashcards

Area of a Square

A square’s area is side length squared; A = s².

Signup and view all the flashcards

Diagonal of a Square

The diagonal of a square can be calculated using A² + A² = d².

Signup and view all the flashcards

Rhombus Properties

A rhombus has equal sides, opposite angles equal, and diagonals bisect each other at 90°.

Signup and view all the flashcards

Area of a Rhombus

Area can also be calculated with diagonals; A = (d1 × d2)/2.

Signup and view all the flashcards

Pythagorean Theorem

In a right triangle, a² + b² = c², where c is the hypotenuse.

Signup and view all the flashcards

Symmetry in Geometry

A shape is symmetric if it looks the same when divided by a line.

Signup and view all the flashcards

More Like This

Use Quizgecko on...
Browser
Browser