Quadrilateral Properties
A free Geometry lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Quadrilaterals are four-sided polygons. Parallelograms have two pairs of parallel sides, rectangles add right angles, rhombi add four congruent sides, and squares have both.
What you'll learn
- Classify quadrilaterals
- Use parallelogram properties
- Distinguish rectangles, rhombi, squares, and trapezoids
Worked example
Problem. A quadrilateral has two pairs of parallel sides and four right angles. What is it?
- Two pairs of parallel sides make it a parallelogram.
- Four right angles make it a rectangle.
- It could be a square only if all sides are also congruent.
Answer: rectangle
Practice problems
1. A quadrilateral with two pairs of parallel sides is a...
Choices: Parallelogram · Triangle · Circle · Ray
Show solution
- Warm-up: First identify exactly what the question is asking: A quadrilateral with two pairs of parallel sides is a...
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- This is the definition of a parallelogram.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Parallelogram
2. A parallelogram with four right angles is a...
Choices: Rectangle · Kite only · Trapezoid only · Pentagon
Show solution
- Warm-up: First identify exactly what the question is asking: A parallelogram with four right angles is a...
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Right angles make it a rectangle.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Rectangle
3. A parallelogram with four congruent sides is a...
Choices: Rhombus · Rectangle always · Circle · Scalene triangle
Show solution
- Core Practice: First identify exactly what the question is asking: A parallelogram with four congruent sides is a...
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- A rhombus has all sides congruent.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Rhombus
4. A square is always a...
Choices: Rectangle and rhombus · Trapezoid only · Triangle · Circle
Show solution
- Core Practice: First identify exactly what the question is asking: A square is always a...
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Squares have four right angles and four congruent sides.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: Rectangle and rhombus
5. Consecutive angles in a parallelogram add to what measure?
Show solution
- Challenge: First identify exactly what the question is asking: Consecutive angles in a parallelogram add to what measure?
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Consecutive parallelogram angles are supplementary.
- Check the result by substituting or estimating: the response should match 180 and make sense in the original problem.
Answer: 180
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