Congruent and similar shapes
If two shapes are congruent, they are identical in both shape and size.
Remember: Shapes can be congruent even if one of them has been rotated or reflected.
Which of the shapes in the illustration above are congruent?
Did you get the following pairs?
Remember: Shapes can be congruent even if one of them has been rotated (as in A and G) or reflected (as in C and H).
The symbol means 'is congruent to'.
Two triangles are congruent if one of the following conditions applies:
The three sides of the first triangle are equal to the three sides of the second triangle (the SSS rule: Side Side Side).
Two sides of the first triangle are equal to two sides of the second triangle, and the included angle is equal (the SAS rule: Side Angle Side).
Two angles in the first triangle are equal to two angles in the second triangle, and one (similarly located) side is equal (the AAS rule: Angle Angle Side).
In a right-angled triangle, the hypotenuse and one other side in the first triangle are equal to the hypotenuse and corresponding side in the second triangle (the RHS rule: Right-angled, Hypotenuse, Side).
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