can one tell if two triangles are congruent if they are given only the angles and all of them are congruent to one another? (Example below)
triangle ABC and triangle DEF with angle A congruent to angle D, angle B congruent to angle E, and angle C congruent to angle F
no, they are not congruent, but they are similar.
e.g. a Slide projected on the wall has an image where the corresponding angles of the shapes would be equal, but certainly the shapes would not have the same size.
ok thank you so much. that is what i thought but i was thinking too much into it...again :)
Yes, in the example you provided, if all angles of two triangles are congruent to one another, then the triangles are indeed congruent. This is known as the Angle-Angle-Angle (AAA) congruence criterion.
To understand why this is the case, let's break it down step by step:
1. Start by comparing the first pair of congruent angles: angle A and angle D. This means that these angles have the same measure.
2. Now, let's compare the second pair of angles: angle B and angle E. Since these angles are congruent, they also have the same measure.
3. Finally, compare the third pair of angles: angle C and angle F. If these angles are congruent, it means they have the same measure as well.
By using all three pairs of congruent angles, we can conclude that all three angles of triangle ABC are congruent to the corresponding angles of triangle DEF.
When all angles of two triangles are congruent, it implies that the two triangles have the same shape and size. Therefore, they are congruent.
In summary, for the given example, if all angles of triangle ABC are congruent to the corresponding angles of triangle DEF, then the two triangles are congruent based on the Angle-Angle-Angle (AAA) congruence criterion.