CCSS.Math.Content.4.G.A.2
The Standard
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Common Core State Standards for Mathematics · Geometry
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students examine two-dimensional shapes and use line relationships and angle measures to sort and name them. They identify any triangle containing one 90-degree angle as a right triangle.
What Mastery Looks Like
- Given a mixed set of shapes, a student sorts each by parallel sides, perpendicular sides, and acute, right, or obtuse angles. The student gives evidence for each choice and recognizes a rotated right triangle.
Common Misconceptions
- Students may judge a shape by how it is turned or by its overall look instead of checking its properties. They may confuse parallel and perpendicular sides, or think a right triangle must have a horizontal base.
How to Assess It
- Show a square, trapezoid, acute triangle, and rotated right triangle. Ask students to label parallel and perpendicular sides, identify angle types, and explain which triangle is a right triangle.
Lesson moves
Ways to Teach It
Using craft sticks and paper corner testers, students build polygons, including a right triangle, then label line relationships and angle types.
Have students explain whether one shape can belong to more than one group, using a square or right triangle as evidence.
Play Property Detective: one partner draws a shape card, gives three property clues, and the other names or sketches the shape.
Students photograph or sketch classroom objects, then identify examples of parallel edges, perpendicular edges, and right-triangle shapes.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.4.G.A.1
Students must recognize parallel and perpendicular lines and angle types before classifying shapes by those features.
- CCSS.Math.Content.4.MD.C.5
Understanding angles and their measures supports classifying shapes by angle size and recognizing triangles with right angles.
- CCSS.Math.Content.3.G.A.1
Classifying quadrilaterals by shared attributes supports later classification using parallel lines, perpendicular lines, and angle properties.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.5.G.B.4
Classifying by parallel lines, perpendicular lines, and angle types supports using properties to place figures in nested categories.
- CCSS.Math.Content.5.G.B.3
Classifying figures by lines and angles prepares students to see how shared attributes define categories and carry into subcategories.
- CCSS.Math.Content.6.G.A.1
Recognizing right triangles and perpendicular sides supports decomposing polygons into usable triangles and rectangles for area.
Keep exploring
Related Standards
- CCSS.Math.Content.4.G.A
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
- CCSS.Math.Content.5.G.B
Classify two-dimensional figures into categories based on their properties.
- CCSS.Math.Content.2.G.A.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pe...
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