seegongsik
Saved words
Grade 5 (age 10-11)

grade 5 Congruence & Symmetry

Congruence & Symmetry

Congruent shapes have the same shape and size, so one fits onto the other after a slide, turn, or flip. Fold a sheet in half and cut it, and both sides match; that fold is the axis of symmetry. Matching points sit at the same distance from that axis and face each other. Rotate a triangle to test congruence, then slide the axis and the shape reflects like a mirror.

What is Congruence?

🧩 Two shapes that overlap perfectly
①Same shape and size = congruent
②If one can slide, rotate, or flip to overlap, they are congruent
③All corresponding sides and angles are equal. If side AB matches side DE, those lengths are equal
50
30°

What is Line Symmetry?

🪞 Like a mirror image!
①A shape cut from folded paper is line-symmetric
②The fold line is the axis of symmetry
③This page covers line symmetry only. Point symmetry (a 180° turn about a point) is not shown here
④A circle matches across any diameter, so it has infinitely many axes
50%

Summary

Congruence Condition
≡ : all corresponding sides and angles are equal
If shapes can be matched by slide/flip/rotate, they are congruent
Line Symmetry Property
Distance from axis to each pair of points is equal
Folding along the axis makes the shape overlap
🎯 Key Points
①Congruent: same shape and size
②Symmetric: overlaps when reflected across an axis
③Congruent → corresponding sides/angles all equal
④Line-symmetric shape has ≥ 1 axis
⑤A circle has infinitely many axes!

Examples and Unit Test

Example 1
Two shapes are congruent. If one side of the first is 5 cm, how long is the corresponding side of the other?
1
Congruent shapes have all corresponding sides equal in length.
2
Since one side is 5 cm, the corresponding side is also 5 cm.
▸ 5 cm
Congruent means all corresponding sides and angles are equal.
Example 2
In a line-symmetric figure, a point is 3 cm from the axis. How far is its corresponding point from the axis?
1
In line symmetry, corresponding points are the same distance from the axis.
2
Since one point is 3 cm away, its corresponding point is also 3 cm away.
▸ 3 cm
Folding along the axis makes corresponding points overlap exactly.
Unit Test
Which shape has infinitely many axes of symmetry?
①equilateral triangle
②rectangle
③circle
④square
▸ ③ circle
1
An axis of symmetry is a line along which a folded shape overlaps exactly.
2
For a circle, every line through the center is an axis, so there are infinitely many.
← Previous
Mixed Operations
Next →
Area of Polygons