Question Video: Applying Properties of Congruence to Solve Problems

The two triangles in the given figure are congruent. Work out the area of triangle 𝐴𝐵𝐶.

02:24

Video Transcript

The two triangles in the given figure are congruent. Work out the area of triangle 𝐴𝐵𝐶.

We’re told here that the two triangles are congruent. That means that pairs of corresponding angles will be equal and pairs of corresponding sides will be equal. We’ll need to use this fact to help us work out the area of triangle 𝐴𝐵𝐶.

We can recall that to find the area of a triangle, we multiply half times the base times the perpendicular height. When we look at triangle 𝐴𝐵𝐶, we can see that we don’t know the base length of this triangle, which is why we’ll need to use the fact that this is congruent with triangle 𝐷𝐸𝐹 to help us work out the length of 𝐵𝐶.

In this question, we weren’t given a congruency relationship, so we’ll need to establish which sides correspond to which sides. Let’s start with the hypotenuse, the longest side on triangle 𝐴𝐵𝐶. This will correspond with the longest side or hypotenuse on our other triangle. So, 𝐴𝐶 and 𝐷𝐹 will be congruent.

On triangle 𝐴𝐵𝐶, if we go from the hypotenuse down to the right angle along the line 𝐴𝐵, this corresponds to the same journey or path from the hypotenuse down to the right angle on triangle 𝐷𝐸𝐹. So, 𝐴𝐵 and 𝐷𝐸 will be the same length of 5.1. The final pair of sides 𝐵𝐶 and 𝐸𝐹 will also be congruent, and they’ll be of length 4.1.

We now have enough information to work out the area of triangle 𝐴𝐵𝐶. Filling in the values for our base length of 4.1 and the perpendicular height of 5.1, we’ll have a half times 4.1 times 5.1. We can work out 4.1 times 5.1 by calculating 41 times 51. As our values had a total of two decimal digits, then our answer will also have two decimal digits. Half of 20.91 will give us 10.455. The units here would be square units. This is our answer for the area of triangle 𝐴𝐵𝐶. Note that if we worked out the area of triangle 𝐷𝐸𝐹 instead, we would’ve got the same answer as both of these triangles are congruent.

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