Two triangles with three pairs of congruent angles are congruent
To prove the statement “Two triangles with three pairs of congruent angles are congruent,” we will use the Angle-Angle-Angle (AAA) congruence criterion
To prove the statement “Two triangles with three pairs of congruent angles are congruent,” we will use the Angle-Angle-Angle (AAA) congruence criterion.
AAA congruence states that if two triangles have three pairs of congruent angles, then the triangles are congruent.
To understand why this is the case, let’s break it down step by step:
1. Consider two triangles, Triangle ABC and Triangle DEF, with three pairs of congruent angles. We will label the angles in each triangle with letters (A, B, C for Triangle ABC and D, E, F for Triangle DEF).
2. By definition of congruent angles, we know that Angle A is congruent to Angle D, Angle B is congruent to Angle E, and Angle C is congruent to Angle F.
3. Now, let’s examine the correspondence between the pairs of angles. We have Angle A in Triangle ABC corresponding to Angle D in Triangle DEF, Angle B in Triangle ABC corresponding to Angle E in Triangle DEF, and Angle C in Triangle ABC corresponding to Angle F in Triangle DEF.
4. By the AAA congruence criterion, we can conclude that Triangle ABC is congruent to Triangle DEF.
The reason why AAA congruence works is that if the angles in two triangles are congruent, then the corresponding sides must also be proportional. Therefore, the triangles have the same shape and size, making them congruent.
In summary, if two triangles have three pairs of congruent angles, we can use the AAA congruence criterion to show that the triangles are congruent.
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