Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

2D Figures Study Guide: Properties of Quadrilaterals and Related Shapes, Lecture notes of Elementary Mathematics

A comprehensive study guide on the properties and relationships of various quadrilaterals and related shapes, including squares, rectangles, parallelograms, rhombuses, and kites. It covers commonalities, differences, true statements, and examples, making it an essential resource for students of geometry.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

anuradha
anuradha 🇺🇸

4.6

(9)

240 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
2D Figures Study Guide
1. What do rectangles & squares have in common? What is different?
Both are quadrilaterals, have right angles, two sets of parallel sides, and opposite sides equal. A square always has equal
sides, but a rectangle might not. A square is a rectangle, but a rectangle is not always a square.
2. What do squares, rectangles, parallelograms, and rhombuses have in common?
All are quadrilaterals, opposite sides are equal & have two sets of parallel sides.
3. Put a check mark by the true statements.
All rectangles are squares.
A rhombus is never a square.
All squares are parallelograms.
A rhombus is always a square.
A kite is always a rhombus.
A kite is always a rectangle.
Some quadrilaterals are trapezoids.
A rhombus is never a rectangle.
Some parallelograms are rhombuses.
A rhombus is always a parallelogram.
A kite is always a quadrilateral.
A square is a rhombus with 4 right
angles.
All squares are rectangles.
All rhombuses are rectangles.
All parallelograms are squares.
All rectangles are rhombuses.
All rhombuses are also squares.
A kite is always a square.
A square is a rectangle with four
sides the same length.
All squares & rectangles have
opposite sides that are congruent.
All parallelograms, rectangles, and
squares have opposite angles that
are congruent.
If all 4 sides of a rhombus are equal,
then it is a square.
A square is a parallelogram with four
lines of symmetry.
If all 4 sides of a rectangle are equal,
then it is a square.
If all 4 angles of a rectangle are equal,
then it is a square.
A square is a quadrilateral with
exactly one pair of parallel sides.
If all 4 angles of a parallelogram are
equal, then it is a square.
A scalene triangle can be an obtuse
triangle.
A scalene triangle can be an
equilateral triangle.
An equilateral triangle can be an
obtuse triangle.
An isosceles triangle can be an
equilateral triangle.
4. What is true of both a square and a parallelogram? What is true of a parallelogram, but not a square?
Both have two sets of parallel sides, but a parallelogram does not have to have equal sides or right angles
5. Is a rectangle a parallelogram? Why?
Yes, it has two sets of parallel sides.
6. A square is also a ___rectangle____, _____rhombus___, ___parallelogram____, ____kite____,
and a ____quadrilateral_____.
7. If two squares are put together, what is formed?
rectangle
8. How are a trapezoid and parallelogram related?
Both are quadrilaterals and have at least one set of parallel sides
9. What is the definition of a trapezoid?
A quadrilateral with only one set of parallel sides
10. A parallelogram is also a ______quadrilateral_____. A rhombus is also a _____parallelogram_____.
pf2

Partial preview of the text

Download 2D Figures Study Guide: Properties of Quadrilaterals and Related Shapes and more Lecture notes Elementary Mathematics in PDF only on Docsity!

2D Figures Study Guide

  1. What do rectangles & squares have in common? What is different?

Both are quadrilaterals, have right angles, two sets of parallel sides, and opposite sides equal. A square always has equal

sides, but a rectangle might not. A square is a rectangle, but a rectangle is not always a square.

  1. What do squares, rectangles, parallelograms, and rhombuses have in common?

All are quadrilaterals, opposite sides are equal & have two sets of parallel sides.

  1. Put a check mark by the true statements.

All rectangles are squares. A rhombus is never a square. All squares are parallelograms. A rhombus is always a square. A kite is always a rhombus. A kite is always a rectangle. Some quadrilaterals are trapezoids. A rhombus is never a rectangle. Some parallelograms are rhombuses.

A rhombus is always a parallelogram.

A kite is always a quadrilateral. A square is a rhombus with 4 right angles. All squares are rectangles. All rhombuses are rectangles. All parallelograms are squares. All rectangles are rhombuses. All rhombuses are also squares. A kite is always a square. A square is a rectangle with four sides the same length.

All squares & rectangles have opposite sides that are congruent.

All parallelograms, rectangles, and squares have opposite angles that are congruent. If all 4 sides of a rhombus are equal, then it is a square.

A square is a parallelogram with four lines of symmetry.

If all 4 sides of a rectangle are equal, then it is a square. If all 4 angles of a rectangle are equal, then it is a square.

A square is a quadrilateral with exactly one pair of parallel sides.

If all 4 angles of a parallelogram are equal, then it is a square. A scalene triangle can be an obtuse triangle.

A scalene triangle can be an equilateral triangle.

An equilateral triangle can be an obtuse triangle. An isosceles triangle can be an equilateral triangle.

  1. What is true of both a square and a parallelogram? What is true of a parallelogram, but not a square?

Both have two sets of parallel sides, but a parallelogram does not have to have equal sides or right angles

  1. Is a rectangle a parallelogram? Why?

Yes, it has two sets of parallel sides.

  1. A square is also a rectangle____, _____rhombus, ___parallelogram____, ____kite____,

and a ____quadrilateral_____.

  1. If two squares are put together, what is formed?

rectangle

  1. How are a trapezoid and parallelogram related?

Both are quadrilaterals and have at least one set of parallel sides

  1. What is the definition of a trapezoid?

A quadrilateral with only one set of parallel sides

  1. A parallelogram is also a ______quadrilateral_____. A rhombus is also a _____parallelogram_____.
  1. What is true of all quadrilaterals?

They are four sided polygons.

  1. Complete the chart with as many examples as you can think of.

Polygons Geometric Figures that are NOT polygons Triangle Quadrilateral Pentagon Hexagon Octagon Etc.

Line Ray Oval Circle Point Etc.

  1. Fill in the chart with all of the appropriate quadrilaterals.

Attributes Quadrilateral(s) Opposite sides congruent & parallel, opposite angles congruent

Rhombus, square, rectangle, parallelogram

All sides equal Square, rhombus

2 pairs of opposite parallel sides, 4 congruent sides, 2 obtuse angles, and 2 acute angles

Rhombus

Exactly two pairs of parallel sides Rhombus, square, rectangle, parallelogram

All four sides equal, but no right angles Rhombus

  1. Draw three polygons that have parallel sides and AREN’T quadrilaterals.
  2. What is a polygon?

A closed figure with three or more straight sides

  1. What property must a parallelogram have in order to be called a rectangle?

Right angles

  1. What quadrilaterals can be classified as parallelograms?

Squares, rectangles, rhombuses

  1. Draw a hierarchy diagram that shows how all quadrilaterals are related.

parallelogram

trapezoid^ kite

quadrilateral

square

rectangle rhombus