Question Video: Understanding the Definition of Congruence | Nagwa Question Video: Understanding the Definition of Congruence | Nagwa

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

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The symbol ≅ means that the two objects are congruent. Write a true statement.

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Video Transcript

The symbol congruency means that the two objects are congruent. Write a true statement.

Here, it seems we have a parallelogram 𝐴𝐵𝐶𝐷 and we split it in half, creating two triangles. Here, we have triangle 𝐴𝐵𝐶 and here we have another triangle. These are going to be congruent because 𝐴𝐵 is congruent to 𝐶𝐷 because of the marking; 𝐵𝐶 is congruent to 𝐷𝐴 because of the two marking, and then they share this last side. So of course 𝐴𝐶 is congruent to 𝐴𝐶. So these triangles are congruent by side-side-side; that’s a property.

So we have to write a true statement. So if we said triangle 𝐴𝐵𝐶, we have to be careful how we write the next triangle. So if we go from 𝐴 to 𝐵 to 𝐶, 𝐴 to 𝐵 has the one marking and 𝐵 to 𝐶 has the two marking. So we need to do the same thing for the other triangle — go from the one marking to the two marking. So we will need to go from 𝐶 to 𝐷 for the one marking and then 𝐷 to 𝐴 for the two marking.

So this would be a true statement. Now, it can be written a few different ways. So notice 𝐴 goes with 𝐶, 𝐵 goes with 𝐷, and 𝐶 goes with 𝐴. So we can change the order if we would like as long as we stay consistent.

So if we started with triangle 𝐵𝐶𝐴, we will need to follow that pattern, so triangle 𝐷𝐴𝐶. And then our last option if we would keep going counterclockwise around triangle 𝐴𝐵𝐶 would be 𝐶𝐴𝐵; that would be congruent to triangle 𝐴𝐶𝐷.

Now, we could do the exact same thing going the other direction. However, any of these three would work for a final answer, so all we need to do is to pick one. So triangle 𝐵𝐶𝐴 is congruent to triangle 𝐷𝐴𝐶.

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