# Why does the ASS (or SSA) can't be used to determine triangle congruence?

## Why is not the ALL or LLA a case of congruence between triangles?

This question can raise a lot of doubt. Thus, we will explore the activity in a pratical way, so that the explanation is clearer.

## Opening Remarks

In the worksheet of "Cases of Congruence﻿"﻿ we can see that there are four cases: SAS (side-angle-side), ASA (angle-side-angle), SSS (Side-Side-Side) and AAS (angle-angle-side). It was natural to think that ASS (angle-side-side) or SSA (side-side-angle) would be possible. Why can't we use these situations as congruence cases? In other words: Why is that two triangles, that have a congruent angle, an congruent adjacent side and an opposite congruent side, not necessarily be considered congruent?

## SOLUTION HYPOTHESIS

As the exercise already states, ALL cannot be considered a case of congruence, so we must prove that this is true. In order to prove this, we can simply show a case in which two triangles have a congruent angle, an congruent adjacent side and an opposite congruent side, and are not congruent.

## Analysis

Move points A, B or C and see if the triangles remain congruent. The question is, Would it be possible to build another triangle whose sides are congruent to AC and CB and that also have a congruent angle. Note that this new triangle is not congruent to ΔABC.