Question Video: Understanding the Definition of Congruent Triangles Mathematics • First Year of Preparatory School

Video Transcript

Given that triangle 𝑃𝑄𝑅 is congruent to triangle 𝑇𝑈𝑉, which of the following is certain? Option (A) angle 𝑃 is congruent to angle 𝑇. Option (B) angle 𝑃 is congruent to angle 𝑉. Option (C) angle 𝑅 is congruent to angle 𝑇. Option (D) angle 𝑅 is congruent to angle 𝑈. Or option (E) angle 𝑄 is congruent to angle 𝑉.

We are told here that there are two triangles, 𝑃𝑄𝑅 and 𝑇𝑈𝑉, and these triangles are congruent. We can recall that congruent triangles, like all congruent polygons, have all corresponding pairs of angles congruent and all pairs of corresponding sides congruent.

Now, we don’t know what these triangles look like. They might look like this or even like this. But we know that since they are congruent, they will be the same shape and size. And that brings us to the ordering of the letters, which is very important in a congruency relationship.

If we labeled the vertex 𝑃 at the top of the triangle and the other vertices were labeled in a clockwise direction to give triangle 𝑃𝑄𝑅, then a congruent triangle 𝑇𝑈𝑉 would also need to have the first listed vertex, which is 𝑇, in the same position at the top and labeled clockwise from vertex 𝑇 to 𝑈 to 𝑉. Or if we had vertex 𝑃 at the bottom of the triangle like this and labeled counterclockwise to vertices 𝑄 then 𝑅, the congruent triangle 𝑇𝑈𝑉 would have to have the corresponding vertices in the same position.

We can use the congruency relationship to tell us that angle 𝑃 is congruent to angle 𝑇. Angle 𝑄 is congruent to angle 𝑈. And angle 𝑅 is congruent to angle 𝑉. Looking at the answer options, the only one of our congruent pairs of angles that is listed is given in option (A), that angle 𝑃 is congruent to angle 𝑇.

Option (B) is incorrect because we already know that angle 𝑃 is congruent to angle 𝑇. And only one pair of angles in congruent polygons can be corresponding to one another.

Options (C) and (D) are incorrect because we’ve already established that angle 𝑅 is congruent to angle 𝑉, not angles 𝑇 or 𝑈.

And finally, option (E) is incorrect because angle 𝑄 is congruent to angle 𝑈, not angle 𝑉.

The only certain statement is therefore that angle 𝑃 is congruent to angle 𝑇.