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 β 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 π΄π΅πΆπ· and we split it in half, creating two triangles. Here, we have triangle π΄π΅πΆ and here we have another triangle. These are going to be congruent because π΄π΅ is congruent to πΆπ· because of the marking; π΅πΆ is congruent to π·π΄ because of the two marking, and then they share this last side. So of course π΄πΆ is congruent to π΄πΆ. So these triangles are congruent by side-side-side; thatβs a property.

So we have to write a true statement. So if we said triangle π΄π΅πΆ, we have to be careful how we write the next triangle. So if we go from π΄ to π΅ to πΆ, π΄ to π΅ has the one marking and π΅ to πΆ has the two marking. So we need to do the same thing for the other triangle β go from the one marking to the two marking. So we will need to go from πΆ to π· for the one marking and then π· to π΄ for the two marking.

So this would be a true statement. Now, it can be written a few different ways. So notice π΄ goes with πΆ, π΅ goes with π·, and πΆ goes with π΄. So we can change the order if we would like as long as we stay consistent.

So if we started with triangle π΅πΆπ΄, we will need to follow that pattern, so triangle π·π΄πΆ. And then our last option if we would keep going counterclockwise around triangle π΄π΅πΆ would be πΆπ΄π΅; that would be congruent to triangle π΄πΆπ·.

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 π΅πΆπ΄ is congruent to triangle π·π΄πΆ.

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