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.
