Why is knowing a combination of four pairs of equal sides or angles harantees one of the congruence relationships
5 years ago
Answered By Emanouil B
This question does not make sense because we don't know what geometrical figure is considered. In general, the question is not set quite clear. It should be formulated like this: We know that we have four equal sides/angles in two triangles. Then why these triangles must be congruent?
So let's consider two triangles. Then three pairs of equal angles does not lead to congruent triangles - they may be similar. It means that we need four equal pairs. Of course, if we had three equal pairs with at least one side then it would be enough for congruency of triangles. But, again, if we have three equal angles (no sides) then it's not enough, so the minimum number of equal parts is 4.
Also, it must be "guarantees" but not "harantees".
5 years ago
Answered By Emanouil B
This question does not make sense because we don't know what geometrical figure is considered. In general, the question is not set quite clear. It should be formulated like this: We know that we have four equal sides/angles in two triangles. Then why these triangles must be congruent?
So let's consider two triangles. Then three pairs of equal angles does not lead to congruent triangles - they may be similar. It means that we need four equal pairs. Of course, if we had three equal pairs with at least one side then it would be enough for congruency of triangles. But, again, if we have three equal angles (no sides) then it's not enough, so the minimum number of equal parts is 4.
Also, it must be "guarantees" but not "harantees".