Virginia SOL Math / Geometry / Polygons & Circles

G.PC.1

Properties of Quadrilaterals

What you'll learn

  • Identify properties of parallelograms, rectangles, rhombi, and squares
  • Use properties to find unknown sides, angles, and diagonals
  • Classify a quadrilateral from its properties

Words to know

Parallelogram —
a quadrilateral with both pairs of opposite sides parallel
Rectangle —
a parallelogram with four right angles
Rhombus —
a parallelogram with four equal sides
Diagonal —
a segment joining opposite vertices
Opposite sides —
sides across from each other in a quadrilateral

Why it matters Quadrilateral properties keep frames square, floors level, and doors hanging true in everyday construction and design.

Worked examples

Model ItI do

In parallelogram ABCD the matching tick marks show equal opposite sides. If AB = 12, what is DC, and what is true of angle A and angle C?

In a parallelogram, opposite sides are equal, so DC = AB = 12. Opposite angles are also equal, so angle A = angle C.

Try It TogetherWe do

In a parallelogram, two consecutive angles measure 3x and 2x. Find x.

Consecutive angles of a parallelogram are supplementary: 3x + 2x = 180. So 5x = 180 and x = 36.

Now YouYou do

A quadrilateral has four equal sides and four right angles. What is the most specific name for it?

Match all the properties to one shape. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.In a parallelogram, opposite sides are _____.

  2. 2.How many equal sides does a rhombus have?

  3. 3.A parallelogram has one angle of 65 degrees. Find the opposite angle.

On Level

The core Quick Check from the book.

  1. 1.In a parallelogram, opposite sides are _____.

  2. 2.How many right angles does a rectangle have?

  3. 3.A rhombus has how many equal sides?

  4. 4.Consecutive angles of a parallelogram add to how many degrees?

  5. 5.A parallelogram has one angle of 70 degrees. Find the opposite angle.

Challenge

Stretch your thinking.

  1. 1.In a parallelogram, two consecutive angles measure 4x and 5x. Find x.

  2. 2.A quadrilateral has four equal sides and four right angles. What is its most specific name?

  3. 3.In parallelogram ABCD, angle A measures 110 degrees. Find angle B.