Congruency refers to geometric figures that have the exact same shape and size, regardless of their position, orientation, or arrangement. In daily life, real-world objects like identical floor tiles, the Petronas Twin Towers, or the front and rear tyres of a car exhibit congruent properties.
A side-by-side comparison of valid congruency rules versus conditional rules.
All three pairs of corresponding sides are equal.
Two sides and the included angle are equal.
Two angles and the included side are equal.
Two angles and a non-included side are equal.
Right angle, hypotenuse and one side are equal.
Valid only if areas are equal.
Two geometric shapes are congruent when they have the exact same size and shape. If you place one directly over the other, they overlap completely.
Two polygons are congruent if and only if all corresponding sides have the same length and all corresponding angles have the same size.
If triangle \(ABC\) is congruent to triangle \(PQR\), it is written as \(\Delta ABC \cong \Delta PQR\).
Read the question, answer it in your mind, then press “Check Answer”.
A triangle has sides measuring \(5\text{ cm}\), \(12\text{ cm}\), and \(13\text{ cm}\). Another triangle has sides measuring \(12\text{ cm}\), \(13\text{ cm}\), and \(5\text{ cm}\). Are these two triangles congruent, and which rule justifies it?
Why is Angle-Angle-Angle (AAA) generally insufficient to prove that two triangles are congruent?
In right-angled triangle \(ABC\) (\(\angle B = 90^\circ\)) and right-angled triangle \(DEF\) (\(\angle E = 90^\circ\)), \(AC = DF = 10\text{ cm}\) and \(AB = DE = 6\text{ cm}\). State the special congruency rule that proves \(\Delta ABC \cong \Delta DEF\).
Two shapes with the same area are always congruent.
Having the same area does not mean shapes are congruent. A rectangle of \(4\text{ cm} \times 9\text{ cm}\) and a rectangle of \(6\text{ cm} \times 6\text{ cm}\) both have an area of \(36\text{ cm}^2\), but their side dimensions and shapes differ completely.
If two shapes are flipped or rotated, they are no longer congruent.
Congruence depends strictly on shape and size. Position, orientation, translation, rotation, and reflection do not affect whether two shapes are congruent.
Complete all parts first, then press the check answer button.
1 Which of the following conditions is always valid to determine that two triangles are congruent without needing their areas to be given?
2 Given \(\Delta ABC \cong \Delta PQR\), if \(AB = 7\text{ cm}\), \(BC = 9\text{ cm}\), and \(\angle ABC = 45^\circ\), which statement must be true?
3 The mathematical symbol used to denote that two triangles are congruent is .
4 The special congruence rule for right-angled triangles where the hypotenuse and one corresponding non-hypotenuse side are equal is known as .
Drag each congruency rule to the correct description. On a phone, tap the answer choice first, then tap the description box.
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