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. In Geometry Foundations, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
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.
- Connect the result back to Quadrilateral Properties so the geometric relationship is explicit.
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.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
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.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
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.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
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.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
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.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
Answer: 180
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