Virginia SOL Math / Grade 7 / Measurement & Geometry

7.MG.3

Quadrilaterals: Sides & Angles

What you'll learn

  • Compare and classify quadrilaterals by their properties
  • Find unknown side lengths using properties of quadrilaterals
  • Find unknown angles knowing the angle sum is 360 degrees

Words to know

Quadrilateral —
a polygon with four sides
Parallelogram —
a quadrilateral with both pairs of opposite sides parallel
Rectangle —
a parallelogram with four right angles
Rhombus —
a parallelogram with four equal sides
Trapezoid —
a quadrilateral with exactly one pair of parallel sides

Why it matters Knowing the properties of quadrilaterals lets us find missing measures in designs, floor plans, and construction without measuring every part.

Worked examples

Model ItI do

Three angles of a quadrilateral are 90, 90, and 100 degrees. Find the fourth angle.

The four angles of a quadrilateral add to 360 degrees. Add the known angles: 90 + 90 + 100 = 280. Subtract: 360 minus 280 = 80 degrees.

Try It TogetherWe do

In a parallelogram, one side is 7 cm. What is the length of the opposite side?

Opposite sides of a parallelogram are equal in length, so the opposite side is also 7 cm.

Now YouYou do

Three angles of a quadrilateral are 70, 110, and 95 degrees. Find the fourth angle.

Subtract the sum of the three angles from 360 degrees. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.What is the sum of the interior angles of a quadrilateral?

  2. 2.In a parallelogram, one side is 6 cm. What is the length of the opposite side?

  3. 3.Which quadrilateral has four equal sides and four right angles?

On Level

The core Quick Check from the book.

  1. 1.What is the sum of the interior angles of a quadrilateral?

  2. 2.In a rectangle, one side is 9 cm. What is the opposite side?

  3. 3.Three angles are 80, 100, and 90 degrees. Find the fourth angle.

  4. 4.Which quadrilateral has four equal sides and four right angles?

  5. 5.Opposite sides of a parallelogram are 5 and x. Find x.

Challenge

Stretch your thinking.

  1. 1.Three angles of a quadrilateral are 85, 95, and 120 degrees. Find the fourth angle.

  2. 2.In a parallelogram, one angle is 70 degrees. Find the measure of the angle next to it.

  3. 3.A rhombus has a perimeter of 36 cm. What is the length of each side?