GCSE(F), GCSE(H),

A **congruent** triangle means that it is the same size as another triangle. However, the congruent triangle may be rotated or reflected, and may not *look* the same.

A **similar** triangle is a triangle that has the same angles, but has different lengths of sides. Note that each side of a similar triangle is in the same ratio as the corresponding side on the other triangle.

A corresponding triangle may be found by checking conditions of congruence. These are:

All three sides equal (side-side-side, or SSS)

Two sides, and the included angle (between the two sides) are all equal (side-angle-side, or SAS)

Two angles and a corresponding side - the same side on each triangle - are equal (angle-angle-side, or AAS)

For a right-angled triangle, the hypotenuse and one other side are equal (right angle - hypotenuse - side, or RHS)

1. Are these two triangle congruent?

Answer: No

Checking using SAS (side - angle - side); one of the sides that is linked to the given angle is not the same as the corresponding side on the other triangle.

2. Are all right-angles triangles with shorter sides of 3cm and 4cm congruent?

Answer: Yes

From Pythagoras, the hypotenuse on each of these triangles will be 5cm. Using RHS - it is a right angled triangle, the hypotenuse is 5cm and at least one of the other sides is the same length on each triangle.

Our iOS app has over 1,000 questions to help you practice this and many other topics.

Available to download free on the App Store.

Available to download free on the App Store.