Question

Tyler claims that if two triangles each have a side length of 11 units and a side length of 8 units, and also an angle measuring 100∘, they must be identical to each other. Do you agree? Explain your reasoning.

Answer 1

No, it is possible to build two different triangles with these measurements. For example: (see picture)

Answer 2

Yes I agree ! both triangles are identical by By SAS ( Side Angle Side ) congruence or SSA ( Side Side Angle ) congruence depending on angle .

Explanation:

Here we have , Tyler claims that if two triangles each have a side length of 11 units and a side length of 8 units, and also an angle measuring 100∘, they must be identical to each other. We need to find is this statement true or not !

According to Tyler , there are two triangles , Parameters are given as :

For triangle 1 :

`a=11\\b=8\\x=100` , where a , b are sides of triangle and x is the angle !

For triangle 2 :

`c=11\\d=8\\y=100` , where c , d are sides of triangle and y is the angle !

On comparing both we get that

`a=c\\b=d\\x=y`

Hence , By SAS ( Side Angle Side ) congruence or SSA ( Side Side Angle ) depending on angle , we can say that both are congruent .

Therefore , Yes I agree ! both triangles are identical by By SAS ( Side Angle Side ) congruence or SSA ( Side Side Angle ) congruence depending on angle .