### Video Transcript

Find the lengths of line segment πΆπ΅ and line segment π΄π·.

In the diagram, we can see that there are two triangles: triangle π΅πΆπ· and triangle π΄π΅π·. In the diagram, we can see that there are two angles that are denoted with one single arc. Thatβs the angle πΆπ΅π· in triangle π΅πΆπ· 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·πΆ is equal to the measure of π΅π·π΄. Letβs 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΅πΆπ· 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 thatβs 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΅πΆπ· and triangle π΄π΅π· are congruent using the angle-side-angle criterion.

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

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