Consider two right-angled triangles where the lengths of the two perpendicular sides in one triangle are equal to the lengths of the corresponding sides in the other. Are these triangles congruent?
This problem has given us a lot of information to answer a simple question, are these triangles congruent? Let’s swap through the information sketching out the triangles to determine if these two triangles are congruent or not. The first thing we know is that both of these triangles are right-angled triangles.
We can start by just adding two right angles. One of these can be triangle A and the other can be triangle B. Next, we find out the lengths of the two perpendicular sides are equal in both of these triangles. One side can measure three centimetres. The other segment that makes up the right angle in both of these triangles could measure four centimetres.
Currently, we don’t have triangles though. We just have two right angles made with line segments. You can fill in triangle A with the yellow line and triangle B with the pink line. How should we determine if these triangles are congruent? Congruent figures are always the same shape and the same size. These two figures — triangle A and triangle B — are the same shape. They’re both right triangles.
But how can we determine if they are the same size? Well, one thing we could do is measure our third side. If each of these triangles have three sides that measure the same lengths, they are exactly the same size. If we measure our third side, the third side of triangle A is five centimeters and the third side of triangle B is five centimeters. This means triangle A has side lengths three, four, five and triangle B has side lengths three, four, five.
These two triangles are exactly the same size. Same shape, same size make congruent figures. By carefully drawing out two figures and measuring them with a ruler, we find the description of these triangles produce two congruent figures.