In this Grade 6 lesson from Saxon Math, Course 1, students learn to classify quadrilaterals by the characteristics of their sides and angles, distinguishing between trapezoids, parallelograms, rhombuses, rectangles, and squares. Students explore the hierarchical relationships among these shapes, such as how a square is a special type of rectangle, which is a special type of parallelogram. The lesson also introduces the prefix quadri- and reinforces polygon vocabulary introduced in earlier chapters.
Section 1
📘 Classifying Quadrilaterals
Quadrilaterals are four-sided polygons that can be sorted, or classified, by the characteristics of their sides and angles.
A quadrilateral is a polygon with four sides.
This is the foundation for identifying shapes. Next, you'll use these definitions to analyze relationships between quadrilaterals in worked examples and practice problems.
Section 2
Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides. Special types include the rhombus (equal sides), rectangle (right angles), and square (equal sides and right angles).
Think of a parallelogram as the parent of a shape family! It’s a tilted rectangle. If you make its sides equal, you get a rhombus. If you straighten its corners to 90 degrees, you get a rectangle. Do both, and you have the super-special square! Every square is both a rectangle and a rhombus, making it the overachiever of the family.
Section 3
Justify
To justify a statement, you must determine if it is always true. If you can find a single case where the statement is not true (a counterexample), then the entire statement is considered false.
Think like a detective proving a rule! To show a statement like “All birds can fly” is false, you don’t need to check every bird. You just need to find one that can't, like a penguin. In geometry, finding one shape that breaks the rule, such as a slanted parallelogram that isn't a rectangle, is enough evidence to declare the statement false.
Section 4
Parallelogram vs. Trapezoid
A parallelogram is a quadrilateral with two pairs of parallel sides. A trapezoid is a quadrilateral with exactly one pair of parallel sides.
It's all about parallel lines! A parallelogram is like a box that got pushed over—both pairs of opposite sides stay parallel no matter what. A trapezoid is different; it’s like a section of a pyramid. Only one pair of sides (usually the top and bottom) are parallel, while the other two sides are on a collision course if you extend them.
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Section 1
📘 Classifying Quadrilaterals
Quadrilaterals are four-sided polygons that can be sorted, or classified, by the characteristics of their sides and angles.
A quadrilateral is a polygon with four sides.
This is the foundation for identifying shapes. Next, you'll use these definitions to analyze relationships between quadrilaterals in worked examples and practice problems.
Section 2
Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides. Special types include the rhombus (equal sides), rectangle (right angles), and square (equal sides and right angles).
Think of a parallelogram as the parent of a shape family! It’s a tilted rectangle. If you make its sides equal, you get a rhombus. If you straighten its corners to 90 degrees, you get a rectangle. Do both, and you have the super-special square! Every square is both a rectangle and a rhombus, making it the overachiever of the family.
Section 3
Justify
To justify a statement, you must determine if it is always true. If you can find a single case where the statement is not true (a counterexample), then the entire statement is considered false.
Think like a detective proving a rule! To show a statement like “All birds can fly” is false, you don’t need to check every bird. You just need to find one that can't, like a penguin. In geometry, finding one shape that breaks the rule, such as a slanted parallelogram that isn't a rectangle, is enough evidence to declare the statement false.
Section 4
Parallelogram vs. Trapezoid
A parallelogram is a quadrilateral with two pairs of parallel sides. A trapezoid is a quadrilateral with exactly one pair of parallel sides.
It's all about parallel lines! A parallelogram is like a box that got pushed over—both pairs of opposite sides stay parallel no matter what. A trapezoid is different; it’s like a section of a pyramid. Only one pair of sides (usually the top and bottom) are parallel, while the other two sides are on a collision course if you extend them.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter