Grade 5 (age 10-11)

Congruence & Symmetry

Congruent shapes have the same shape and size, so one fits right onto the other after a slide, turn, or flip. Fold a paper in half and cut it, and both sides match, with the fold line acting as the axis of symmetry. Here you rotate a triangle to test congruence, then slide the axis to watch a shape reflect like a mirror.

What is Congruence?

🧩 Two shapes that overlap perfectly

①Same shape and size = congruent

②If one can slide, rotate, flip to overlap → congruent

③All corresponding sides and angles are equal!

Translation50

Rotation angle30°

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'

③Each point has a partner the same distance from the axis!

Axis position50%

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?

Congruent shapes have all corresponding sides equal in length.

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?

In line symmetry, corresponding points are the same distance from the axis.

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

An axis of symmetry is a line along which a folded shape overlaps exactly.

For a circle, every line through the center is an axis, so there are infinitely many.

← Previous

Decimal Operations

Polygon Area