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Properties of Quadrilaterals

Parallelograms, rectangles, rhombi, squares, and trapezoids

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Properties of Quadrilaterals

Parallelogram

A quadrilateral with both pairs of opposite sides parallel.

Properties:

  • Opposite sides are congruent
  • Opposite angles are congruent
  • Consecutive angles are supplementary
  • Diagonals bisect each other

Rectangle

A parallelogram with four right angles.

Additional properties:

  • All properties of parallelograms
  • Diagonals are congruent

Rhombus

A parallelogram with four congruent sides.

Additional properties:

  • All properties of parallelograms
  • Diagonals are perpendicular
  • Diagonals bisect the angles

Square

A parallelogram that is both a rectangle and a rhombus.

Properties:

  • Four congruent sides
  • Four right angles
  • Diagonals are congruent and perpendicular
  • Diagonals bisect the angles

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Parts:

  • Bases: the parallel sides
  • Legs: the non-parallel sides
  • Midsegment: connects midpoints of legs, length = b1+b22\frac{b_1 + b_2}{2}

Isosceles Trapezoid

A trapezoid with congruent legs.

Properties:

  • Base angles are congruent
  • Diagonals are congruent

📚 Practice Problems

1Problem 1easy

❓ Question:

In parallelogram ABCD, ∠A=65°\angle A = 65°. Find ∠C\angle C.

💡 Show Solution

In a parallelogram, opposite angles are congruent.

Since ∠A\angle A and ∠C\angle C are opposite: ∠C=∠A=65°\angle C = \angle A = 65°

Answer: ∠C=65°\angle C = 65°

2Problem 2medium

❓ Question:

A trapezoid has bases of length 8 and 14. Find the length of the midsegment.

💡 Show Solution

The midsegment of a trapezoid equals the average of the bases:

M=b1+b22M = \frac{b_1 + b_2}{2}

M=8+142=222=11M = \frac{8 + 14}{2} = \frac{22}{2} = 11

Answer: The midsegment is 11

3Problem 3hard

❓ Question:

In rhombus PQRS, diagonal PR = 16 and diagonal QS = 12. Find the length of one side of the rhombus.

💡 Show Solution

In a rhombus, diagonals are perpendicular and bisect each other.

The diagonals split the rhombus into 4 right triangles.

Half-diagonals:

  • Half of PR = 16/2=816/2 = 8
  • Half of QS = 12/2=612/2 = 6

Use Pythagorean Theorem: s2=82+62s^2 = 8^2 + 6^2 s2=64+36=100s^2 = 64 + 36 = 100 s=10s = 10

Answer: Each side is 10

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❓ Frequently Asked Questions

What is Properties of Quadrilaterals?▾
Parallelograms, rectangles, rhombi, squares, and trapezoids
How can I study Properties of Quadrilaterals effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 3 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Properties of Quadrilaterals study guide free?▾
Yes — all study notes, flashcards, and practice problems for Properties of Quadrilaterals on Study Mondo are free to access. No account is needed.
What course covers Properties of Quadrilaterals?▾
Properties of Quadrilaterals is part of the Geometry course on Study Mondo, specifically in the Quadrilaterals and Polygons section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Properties of Quadrilaterals?▾
Yes, this page includes 3 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.