Grade 7 students in Saxon Math Course 2 learn to identify and name polygons by their number of sides, distinguish between regular and irregular polygons, and understand the concepts of similar and congruent figures. The lesson covers polygon vocabulary including vertices, naming conventions using vertex letters, and how similar figures share the same shape while congruent figures share both the same shape and size.
Section 1
📘 Polygons, Similar and Congruent
Polygons are closed shapes with straight sides. They can be similar (same shape, different size) or congruent (same shape and size).
Soon, we'll use these rules in worked examples to identify polygons and compare their matching parts.
Section 2
Polygon
When three or more line segments are connected to enclose a portion of a plane, a polygon is formed.
A triangle is a polygon because it's a closed, 2D shape with 3 straight sides.
A circle is not a polygon because its boundary is curved, not made of line segments.
An open box is not a polygon because it is a 3D figure, not a plane figure.
Think of a polygon as a flat, closed shape made entirely of straight lines. It’s like building a fence where all the pieces are straight and they all connect to form a complete enclosure with no gaps. If your shape has any curves, isn't fully closed, or exists in 3D like a box, it's not a polygon!
Section 3
Similar Figures
Two figures are similar if they have the same shape even though they may vary in size.
A triangle with sides 3, 4, 5 is similar to one with sides 6, 8, 10 because each side is doubled.
All squares are similar because they all have four angles and proportional sides.
A tall, skinny rectangle is not similar to a short, wide rectangle because their side ratios differ.
Imagine you have a favorite photo and you use a photocopier to shrink or enlarge it. The new photo is a different size, but everyone in it has the same proportions—that's similarity! Similar figures have matching angles, but their side lengths are scaled up or down by the same factor. They are proportional copies of each other.
Section 4
Congruent Figures
Figures that are the same shape and size are not only similar, they are also congruent.
Two triangles are congruent if all three corresponding sides and all three corresponding angles are equal.
A 3-inch by 5-inch rectangle is congruent to another 3-inch by 5-inch rectangle, even if one is rotated.
A square with 2-inch sides is similar to a square with 4-inch sides, but they are not congruent.
Congruent figures are identical twins! They are not just the same shape; they have the exact same side lengths and angle measures. You could cut one out and place it perfectly on top of the other, though you might need to rotate or flip it first. Think of them as perfect clones of each other in every geometric way.
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Section 1
📘 Polygons, Similar and Congruent
Polygons are closed shapes with straight sides. They can be similar (same shape, different size) or congruent (same shape and size).
Soon, we'll use these rules in worked examples to identify polygons and compare their matching parts.
Section 2
Polygon
When three or more line segments are connected to enclose a portion of a plane, a polygon is formed.
A triangle is a polygon because it's a closed, 2D shape with 3 straight sides.
A circle is not a polygon because its boundary is curved, not made of line segments.
An open box is not a polygon because it is a 3D figure, not a plane figure.
Think of a polygon as a flat, closed shape made entirely of straight lines. It’s like building a fence where all the pieces are straight and they all connect to form a complete enclosure with no gaps. If your shape has any curves, isn't fully closed, or exists in 3D like a box, it's not a polygon!
Section 3
Similar Figures
Two figures are similar if they have the same shape even though they may vary in size.
A triangle with sides 3, 4, 5 is similar to one with sides 6, 8, 10 because each side is doubled.
All squares are similar because they all have four angles and proportional sides.
A tall, skinny rectangle is not similar to a short, wide rectangle because their side ratios differ.
Imagine you have a favorite photo and you use a photocopier to shrink or enlarge it. The new photo is a different size, but everyone in it has the same proportions—that's similarity! Similar figures have matching angles, but their side lengths are scaled up or down by the same factor. They are proportional copies of each other.
Section 4
Congruent Figures
Figures that are the same shape and size are not only similar, they are also congruent.
Two triangles are congruent if all three corresponding sides and all three corresponding angles are equal.
A 3-inch by 5-inch rectangle is congruent to another 3-inch by 5-inch rectangle, even if one is rotated.
A square with 2-inch sides is similar to a square with 4-inch sides, but they are not congruent.
Congruent figures are identical twins! They are not just the same shape; they have the exact same side lengths and angle measures. You could cut one out and place it perfectly on top of the other, though you might need to rotate or flip it first. Think of them as perfect clones of each other in every geometric way.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter