Virginia SOL 6.MG.4.d
The Standard
Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles.
Virginia Standards of Learning for Mathematics · The student will determine congruence of segments, angles, and polygons.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare corresponding side lengths and angle measures in two polygons. They decide whether the figures are the same size and shape, regardless of position or orientation.
What Mastery Looks Like
- Students match corresponding vertices, sides, and angles, even when a figure is turned or flipped. They justify congruence using every given measure or identify a mismatch that proves noncongruence.
Common Misconceptions
- Students may judge figures by appearance, orientation, area, or perimeter. They may compare side lengths but ignore angles, or match sides and angles in the wrong order.
How to Assess It
- Give two labeled quadrilaterals, with one turned, and ask: “Are they congruent? List the matching vertices and cite the measurements that prove your answer.”
Lesson moves
Ways to Teach It
Give pairs of paper polygons for students to measure, cut out, rotate, flip, and test by placing one directly over the other.
Ask students to explain why equal perimeter does not prove two polygons are congruent, using a drawn counterexample.
Run a card sort where students match rotated polygon diagrams by corresponding side and angle measures, then label matching vertices.
Compare two floor tile designs and decide whether one tile could replace another exactly, using labeled side lengths and angle measures.
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Related Standards
- 7.MG.2.a
Identify corresponding congruent angles of similar quadrilaterals and triangles, through the use of geometric markings.
- 6.MG.4
The student will determine congruence of segments, angles, and polygons.
- 5.MG.3.c
Identify congruent sides and right angles using geometric markings to denote properties of triangles.
- 6.MG.4.c
Determine the congruence of segments, angles, and polygons given their properties.
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