In Saxon Math Intermediate 4, Grade 4 students learn to identify similar and congruent figures by understanding that similar figures share the same shape while congruent figures share both the same shape and the same size. The lesson uses triangles and rectangles to illustrate how figures can be similar but not congruent when their sizes differ, and introduces the concept that a similar figure is essentially a scaled version of another. Students practice classifying geometric figures and apply these concepts to real-world examples such as road signs.
Section 1
📘 Similar and Congruent Figures
Figures that are the same shape are similar. Figures that are the same shape and the same size are congruent.
Next, you’ll apply these definitions to identify similar and congruent shapes among triangles, rectangles, and real-world signs.
Section 2
Similar
Figures that are the same shape are similar. This means all their corresponding angles are equal, and their corresponding sides are proportional. You can think of a similar figure as a perfectly scaled-up or scaled-down version of the original, like looking at it through a magnifying glass or from far away.
A triangle with side lengths is similar to a triangle with side lengths .
A small rectangular photo measuring inches is similar to a large poster of the same photo measuring inches.
Think of it like a photo you zoom in or out on! The image changes size, but the shape stays the same. If one shape is just a magnified version of another, they are similar. They are shape-twins, but not necessarily size-twins.
Section 3
Congruent
Figures that are the same shape and the same size are congruent. To be congruent, two figures must have all corresponding sides of the same length and all corresponding angles of the same measure. If you can place one figure directly on top of the other so that they match up perfectly, they are congruent.
Two squares are congruent if their side lengths are both cm.
Two triangles are congruent if you can rotate or flip one to fit perfectly on top of the other.
Congruent figures are perfect clones or identical twins! If you could cut one out with scissors, it would fit exactly over the other one with no overlap or gaps. They have the same shape and, critically, the exact same size.
Section 4
All squares are similar
All squares are similar because they all share the exact same shape: four right angles and four sides of equal length. The only attribute that can differ between any two squares is the length of their sides, which is just a matter of scale. Therefore, any square is simply a scaled version of another, fitting the definition of similarity.
A square with a side length of inches is similar to a square with a side length of feet.
A small, square sticky note is similar in shape to a large, square window pane.
Two different-sized square-shaped stamps are similar to each other.
Imagine a tiny sugar cube and a giant Rubik's Cube. Despite the huge size difference, they both have that perfect 'squareness.' You can always magnify the sugar cube until it looks just like the Rubik's Cube. That's why every single square in the universe is similar to every other one!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
📘 Similar and Congruent Figures
Figures that are the same shape are similar. Figures that are the same shape and the same size are congruent.
Next, you’ll apply these definitions to identify similar and congruent shapes among triangles, rectangles, and real-world signs.
Section 2
Similar
Figures that are the same shape are similar. This means all their corresponding angles are equal, and their corresponding sides are proportional. You can think of a similar figure as a perfectly scaled-up or scaled-down version of the original, like looking at it through a magnifying glass or from far away.
A triangle with side lengths is similar to a triangle with side lengths .
A small rectangular photo measuring inches is similar to a large poster of the same photo measuring inches.
Think of it like a photo you zoom in or out on! The image changes size, but the shape stays the same. If one shape is just a magnified version of another, they are similar. They are shape-twins, but not necessarily size-twins.
Section 3
Congruent
Figures that are the same shape and the same size are congruent. To be congruent, two figures must have all corresponding sides of the same length and all corresponding angles of the same measure. If you can place one figure directly on top of the other so that they match up perfectly, they are congruent.
Two squares are congruent if their side lengths are both cm.
Two triangles are congruent if you can rotate or flip one to fit perfectly on top of the other.
Congruent figures are perfect clones or identical twins! If you could cut one out with scissors, it would fit exactly over the other one with no overlap or gaps. They have the same shape and, critically, the exact same size.
Section 4
All squares are similar
All squares are similar because they all share the exact same shape: four right angles and four sides of equal length. The only attribute that can differ between any two squares is the length of their sides, which is just a matter of scale. Therefore, any square is simply a scaled version of another, fitting the definition of similarity.
A square with a side length of inches is similar to a square with a side length of feet.
A small, square sticky note is similar in shape to a large, square window pane.
Two different-sized square-shaped stamps are similar to each other.
Imagine a tiny sugar cube and a giant Rubik's Cube. Despite the huge size difference, they both have that perfect 'squareness.' You can always magnify the sugar cube until it looks just like the Rubik's Cube. That's why every single square in the universe is similar to every other one!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter