# Video: Proving Results Using Triangle Congruence

In the given quadrilateral, 𝐴𝐹 and 𝐵𝐹 have the same length and 𝐸𝐹 and 𝐶𝐹 have the same length. Which angle has the same measure as ∠𝐴𝐹𝐸? Hence, are triangles 𝐴𝐹𝐸 and 𝐵𝐹𝐶 congruent? If yes, state which congruence criterion proves this.

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### Video Transcript

In the given quadrilateral, 𝐴𝐹 and 𝐵𝐹 have the same length and 𝐸𝐹 and 𝐶𝐹 have the same length. Which angle has the same measure as angle 𝐴𝐹𝐸? Hence, are triangles 𝐴𝐹𝐸 and 𝐵𝐹𝐶 congruent? If yes, state which congruence criterion proves this.

In this diagram, we can see that there’s a quadrilateral which has some triangles within it. We’re told that there are some line segments which have the same length. So it’s always worthwhile putting this onto a diagram if they’re not already marked. 𝐴𝐹 and 𝐵𝐹 are the same length and 𝐸𝐹 and 𝐶𝐹 are the same length. In the second question, we’ll look at congruency. But the first question asks us about angle measures. Which angle would be the same as angle 𝐴𝐹𝐸? We’re not given any angle measurements in this diagram, but we should recall that angles which are vertically opposite will be equal. So angle 𝐵𝐹𝐶 would also be the same measurement. And that’s our answer for the first part of the question.

In the second part of the question, we need to check if triangles 𝐴𝐹𝐸 and 𝐵𝐹𝐶 are congruent. So let’s note down any sides or angles that we know are congruent. We were told in the question that 𝐴𝐹 and 𝐵𝐹 are the same length. We have shown in the first part of the question that we have two congruent angles, angle 𝐴𝐹𝐸 and angle 𝐵𝐹𝐶. And we were told that sides 𝐸𝐹 and 𝐶𝐹 are the same length.

And so, we have two pairs of congruent sides equal and a pair of congruent angles. Importantly, the angle is included between the two sides, which means that we can use the SAS congruency criterion. If the angle wasn’t included between the two sides, then it wouldn’t be sufficient to show congruence. So our answer for this part of the question is, yes, these two triangles are congruent, and we use the SAS criterion.