Hey folks! I recently made a project about the congruence of triangles in an advanced way. The one of the topic is SSA (Side-side-angle). Teachers always say that SSA cannot prove two triangles are congruent (the explanation is here), but I want to tell you guys about SSA can prove the congruence of two triangles with some conditions. Let's check this out!
At first, let a triangle be such that we only know about the length of and the size of , by the sine formula, we can show that
From here there are two cases:
There are only possibility of , which is . Then, we know the size of and the length of , so we can show that there are only possible triangle by applying . Therefore, we can conclude that when , which means , is true.
Then, there are possibilities of , and . Hence, we need to consider to find out more conditions of proving . By the angle sum of triangle, . We will consider two cases about
. Then, can only be , so there are only possible triangle similarly. Therefore, we can conclude that when , is true.
Do you notice that? When , it is the same case as RHS (Right angle-hypotenuse-side) or HL (Hypotenuse-leg)
. It is true when . Because of we want to have possibility of , we need to ignore the other possibility of , which we get the inequality below:
Therefore, we can conclude that when , is true.
To sum up, there is a triangle given the length of and the size of , if this triangle has one or more of the conditions below, then is true:
I hope it will help you guys! Please comment below if you had something to say about this article. Thank you!