The SSA (Side-Side-Angle) Congruence Rule

Blog Introduction: In geometry, two triangles are said to be "congruent" if they have the same size and shape. That is, all three sides of one triangle must be equal to the corresponding sides of the other triangle. There are a few different ways to establish congruence between two triangles, and today we're going to focus on the SSA (Side-Side-Angle) congruence rule. 

How to Use the SSA Congruence Rule

In order to use the SSA congruence rule, you must be given two triangles and told that at least one angle is congruent. From there, you need to determine whether the given information is sufficient to prove that the two triangles are indeed congruent. 

There are a few things you need to keep in mind when using the SSA congruence rule. First, remember that "congruent" means "equal in size and shape." So, in order for two triangles to be considered congruent using this rule, not only do their corresponding sides need to be equal—their corresponding angles also need to be equal. Second, it's important to note that the SSA congruence rule can only be used when given information about two angles and a side that is not between those angles; if you're given information about a side that is between two angles, you can't use this rule. 

Let's look at an example. Say we're given information about Triangle ABC and Triangle DEF, as well as the fact that Angle A is congruent to Angle D. Is this enough information to say that Triangle ABC is congruent to Triangle DEF? No—we don't know anything about the other angles or sides of either triangle, so we can't make that conclusion. 

Now let's say we're given information about Triangle ABC and Triangle DEF, as well as the fact that Angle A is congruent to Angle D and Side AB is congruent to Side DE. Is this enough information to say that Triangle ABC is congruent to Triangle DEF? Yes—this time we know that not only are two angles equal, but we also know that corresponding sides are equal. Therefore, we can conclude that these two triangles are indeed congruent. 

Conclusion: 

The SSA (Side-Side-Angle) congruence rule states that in order for two triangles to be considered congruent, they must have corresponding sides that are equal in length and corresponding angles that are equal in measure. This rule can only be used when given information about two angles and a side that is not between those angles; if you're given information about a side that is between two angles, you can't use this rule. Now go out there and start proving some triangles congruent!

FAQ

What is La congruence theorem?

The congruence theorem states that in order for two triangles to be considered congruent, they must have corresponding sides that are equal in length and corresponding angles that are equal in measure. This rule can only be used when given information about two angles and a side that is not between those angles; if you're given information about a side that is between two angles, you can't use this rule.

What is SSA congruence rule?

The SSA (Side-Side-Angle) congruence rule states that in order for two triangles to be considered congruent, they must have corresponding sides that are equal in length and corresponding angles that are equal in measure. This rule can only be used when given information about two angles and a side that is not between those angles; if you're given information about a side that is between two angles, you can't use this rule.