Finding Corresponding Angles: Triangle ABC vs Triangle DEF

Question

Look at the two triangles below:

Angle B is equal to angle E.
Angle A is equal to angle D.

Which angle corresponds to angle C?

00:03 Let's find out what angle matches with angle C.

00:06 Angles are equal, as given in the data.

00:10 The triangles are similar by the angle-angle rule, or A.A.

00:15 So, the matching angle is the last angle, angle F.

00:20 And there you have it, that's how we solve this problem!

As we have two pairs of corresponding angles, we will use the angle-angle theorem for triangle similarity.

Now that we know all angles are equal to each other, we note that the remaining angle that is equal and corresponds to angle C is angle F.

$F$