Virginia SOL 7.MG.3.a.ii
The Standard
Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid: congruence of angle measures, side, and diagonal lengths
Virginia Standards of Learning for Mathematics · The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify which sides, angles, and diagonals must have equal measures in each named quadrilateral. They compare figures and separate properties that are always true from those that only appear true in a drawing.
What Mastery Looks Like
- Students correctly mark guaranteed congruent parts without relying on how a figure looks. They explain, for example, that a rhombus has four congruent sides but does not always have congruent diagonals.
Common Misconceptions
- Students often assume every parallelogram has four equal sides or congruent diagonals. They may also think every trapezoid has congruent legs or angles because examples often look symmetrical.
How to Assess It
- Exit ticket: For a rectangle, rhombus, and parallelogram, list which sides, angles, and diagonals must be congruent, then state one difference.
Lesson moves
Ways to Teach It
Give pairs paper quadrilaterals, rulers, and protractors to measure sides, angles, and diagonals, then label all congruent parts.
Ask students to explain why a square fits the properties of both a rectangle and a rhombus.
Play a property-card sort where students match cards such as “congruent diagonals” or “four congruent sides” to every valid quadrilateral.
Examine photos of windows, tiles, and tabletops, then identify which lengths or angles should match based on each object’s quadrilateral shape.
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