Question Video: Writing a Triangle Congruence Relationship | Nagwa Question Video: Writing a Triangle Congruence Relationship | Nagwa

# Question Video: Writing a Triangle Congruence Relationship Mathematics • First Year of Preparatory School

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Which is the correct congruence from this figure? [A] β³π΄π΅π· β β³π΄π·πΆ [B] β³π΅π·π΄ β β³πΆπ·π΄ [C] β³π΄π΅π· β β³πΆπ·π΄ [D] β³π΄π·π΅ β β³πΆπ·π΄

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### Video Transcript

Which is the correct congruence from this figure? Option (A) triangle π΄π΅π· is congruent to triangle π΄π·πΆ. Option (B) triangle π΅π·π΄ is congruent to triangle πΆπ·π΄. Option (C) triangle π΄π΅π· is congruent to triangle πΆπ·π΄. Option (D) triangle π΄π·π΅ is congruent to triangle πΆπ·π΄.

Here we can see that there are two triangles, π΄π΅π· and π΄πΆπ·. As weβre told that there is some sort of congruence between these two triangles, it would be sensible to list any angles or pairs of sides which are congruent. So letβs take our two triangles, π΄π΅π· and π΄πΆπ·. The angle at π΄π΅π· is marked as congruent with the angle at π΄πΆπ·. So thatβs a pair of congruent angles. In triangle π΄π΅π·, we have this side π΅π· marked as the same length as side πΆπ· in triangle π΄πΆπ·. We can tell this from the one marking on each of these lines. So thatβs a pair of congruent sides. We have another pair of congruent angles. Angle π΅π·π΄ is congruent with angle πΆπ·π΄. So thatβs another pair of congruent angles.

This means that we have found two pairs of corresponding angles congruent and an included pair of corresponding sides congruent. We could then say that these triangles are congruent using the ASA or angle-side-angle rule. We might also notice that we have a line π΄π· which is common to both sides, meaning that weβve actually found another pair of congruent sides. So we could have alternatively said that these triangles are congruent using the side-angle-side rule.

The question has asked us to select the correct congruence for the figure. So what does that mean? You may recall that the order of the letters is important when weβre writing congruence. If we look at the side π΄π΅ in this top triangle, thatβs congruent with our side π΄πΆ on the lower triangle. The length going from π΅π· is congruent with the length πΆπ·. And so we could say that triangle π΄π΅π· is congruent with triangle π΄πΆπ·.

We can also write the letters in a different way. For example, we could start with π΅π· on triangle π΄π΅π·, but then weβd also have to start with the letters πΆπ· in triangle π΄πΆπ·. So we could write the relationship that triangle π΅π·π΄ is congruent to triangle πΆπ·π΄.

We could also start with our letter π· and say that triangle π·π΄π΅ is congruent to triangle π·π΄πΆ. Any of these would be a correct congruence for the figure. However, the only one listed in the answer options is that given in option (B) triangle π΅π·π΄ is congruent to triangle πΆπ·π΄.

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