# Question Video: Using the Congruence between Triangles to Find the Length of Line Segments Mathematics • 8th Grade

Find the lengths of line segment πΆπ΅ and line segment π΄π·.

02:21

### Video Transcript

Find the lengths of line segment πΆπ΅ and line segment π΄π·.

In the diagram, we can see that there are two triangles: triangle π΅πΆπ· and triangle π΄π΅π·. In the diagram, we can see that there are two angles that are denoted with one single arc. Thatβs the angle πΆπ΅π· in triangle π΅πΆπ· and the angle π΄π΅π· in triangle π΄π΅π·. And since the angles are denoted in the same way, this means that the measure of these angles are equal to each other.

We have another pair of angles that are noted by a double arc. So we can say that the measure of angle π΅π·πΆ is equal to the measure of π΅π·π΄. Letβs have a look at the lines in our triangles. We can see that the line π΅π· occurs in both triangles. And since this line is common to both triangles, we can say that the line π΅π· in triangle π΅πΆπ· is equal to the line π΅π· in triangle π΄π΅π·.

So now we know that our two triangles have two pairs of corresponding angles equal and a corresponding side equal. We can notice that the corresponding side thatβs equal is in between the pairs of corresponding angles equal. And we can note this as angle-side-angle or ASA. And we can say that triangle π΅πΆπ· and triangle π΄π΅π· are congruent using the angle-side-angle criterion.

Letβs now see how we can use the fact that the triangles are congruent to find the lengths of line segment πΆπ΅ and line segment π΄π·. So line segment πΆπ΅ in triangle π΅πΆπ· must be equal to line segment π΄π΅ in triangle π΄π΅π·. We can see that line segment π΄π΅ is labelled as 20 centimetres. Therefore, πΆπ΅ must also be equal to 20 centimetres. Next, to find our line segment π΄π·, we know that the corresponding side in triangle π΅πΆπ· must be the line segment πΆπ·. And since πΆπ· is labelled as 12 centimetres, then π΄π· must also be 12 centimetres.

And so our final answer is line segment πΆπ΅ equals 20 centimetres. Line segment π΄π· equals 12 centimetres.