Look at the two triangles below:
Angle B is equal to angle F.
Angle C is equal to angle D.
Which angle corresponds to angle A?
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Look at the two triangles below:
Angle B is equal to angle F.
Angle C is equal to angle D.
Which angle corresponds to angle A?
We use the angle-angle theorem to simulate triangles.
Let's observe the data we already have:
Angles B and F are equal.
Angle C is equal to angle D.
Therefore, the remaining angles must also be equal: angles A and E.
Is the similarity ratio between the three triangles equal to one?
Look at the given equal angles first! Since angle B = angle F and angle C = angle D, vertices B and F match, and vertices C and D match. This means vertex A must correspond to vertex E.
The position doesn't matter for angle correspondence! Focus on which angles are equal. The angle-angle theorem tells us that triangles with two pairs of equal angles are similar, so the third pair must also be equal.
Corresponding angles must follow the vertex matching pattern. Since B corresponds to F and C corresponds to D, the vertices spell out the pattern: A must correspond to E to maintain proper triangle correspondence.
No! You can use logical reasoning. If two pairs of angles are equal, the Angle-Angle theorem guarantees the triangles are similar, so the third pair of angles must also be equal.
Write out the correspondence: Triangle ABC ~ Triangle ?. Since B = F and C = D, fill in the pattern: Triangle ABC ~ Triangle EFD doesn't work, but Triangle ABC ~ Triangle FDE does! So A corresponds to E.
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