Geometry · Triangles & polygons · 2.4

Quadri- laterals.

Four-sided shapes are named by their sides and angles: a square has 4 equal sides and 4 right angles; a rectangle has right angles with opposite sides equal; a rhombus has 4 equal sides; a parallelogram has opposite sides parallel; a trapezoid has exactly one pair of parallel sides.

01 / THE IDEA

See it work.

Watch the method

Quadrilaterals

Right angles + equal sides → square; one parallel pair → trapezoid.

1 / 2
1

Area of a rectangle

Area is length times width.

l×wl \times w
2

Multiply

Multiply the two dimensions.

NaN×undefined=NaNNaN \times undefined = NaN
— / WHY IT WORKS

The idea underneath.

Sides and corners

Equal sides and right angles separate the special quadrilaterals.

Why it works

A square is the most special — all of the above.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Which quadrilateral has opposite sides equal and 4 right angles?

1

Answer

Rectangle

EX 2medium

Which quadrilateral has opposite sides equal and 4 right angles?

1

Answer

Rectangle

EX 3hard

Which quadrilateral has 4 equal sides but no right angles?

1

Answer

Rhombus

04 / COMMON TRAPS

Where students slip.

Trap

Calling every 4-equal-side shape a square.

Fix

A rhombus also has 4 equal sides but no right angles.

Trap

Confusing trapezoid with parallelogram.

Fix

A trapezoid has only ONE pair of parallel sides.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Which quadrilateral has 4 equal sides and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
C2

Which quadrilateral has exactly one pair of parallel sides?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
C3

Which quadrilateral has opposite sides equal and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
C4

Which quadrilateral has 4 equal sides and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
Apply

Apply (4)

A1

Which quadrilateral has opposite sides equal and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
A2

Which quadrilateral has opposite sides equal and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
A3

Which quadrilateral has exactly one pair of parallel sides?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
A4

Which quadrilateral has 4 equal sides but no right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
Extension

Extension (4)

E1

Which quadrilateral has exactly one pair of parallel sides?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
E2

Which quadrilateral has 4 equal sides and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
E3

Which quadrilateral has 4 equal sides but no right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.
E4

Which quadrilateral has 4 equal sides and 4 right angles?

Need a hint?
  • Check the angles and side lengths.
  • Right angles point to square/rectangle.