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?
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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?
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.
Angle B is equal to 60°
Angle C is equal to 55°
Angle E is equal to 60°
Angle F is equal to 50°
Are these triangles similar?
Look at the given information first! If angle B = angle E and angle A = angle D, then the triangles match in order ABC ↔ DEF, so angle C must equal angle F.
Size doesn't matter for corresponding angles! Similar triangles have the same shape but different sizes, so all corresponding angles are equal regardless of triangle size.
Yes! The Angle-Angle (AA) theorem says if two angles in one triangle equal two angles in another triangle, the triangles are similar and the third angles must also be equal.
Similar triangles have equal angles but different side lengths. Congruent triangles have both equal angles AND equal side lengths.
Write the triangles in the same order as the given equal angles: if B = E and A = D, then ABC corresponds to EDF... wait, that's wrong! Always keep vertex order: ABC ↔ DEF.
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