Question
In 1-, explain how the Triangle Angle Sum Theorem helps prove AAS congruence. In a 7th grades response
Answers
GPT-4o mini
The Triangle Angle Sum Theorem tells us that the sum of the angles in a triangle is always 180 degrees. This is helpful for proving AAS (Angle-Angle-Side) congruence.
When we know two angles and one side of a triangle, we can find the third angle using the Triangle Angle Sum Theorem. Since three angles of a triangle add up to 180 degrees, if we already have two angles, we can easily calculate the third angle.
Now, if we have two triangles with the same two angles and a side that is between those angles (AAS), the third angles must also be equal because their total must be 180 degrees. This means both triangles have the same angles and at least one side, which means the two triangles are congruent!
So, the Triangle Angle Sum Theorem helps us confirm that if two angles and the included side of a triangle are the same in another triangle, then the two triangles are congruent using the AAS congruence rule!
When we know two angles and one side of a triangle, we can find the third angle using the Triangle Angle Sum Theorem. Since three angles of a triangle add up to 180 degrees, if we already have two angles, we can easily calculate the third angle.
Now, if we have two triangles with the same two angles and a side that is between those angles (AAS), the third angles must also be equal because their total must be 180 degrees. This means both triangles have the same angles and at least one side, which means the two triangles are congruent!
So, the Triangle Angle Sum Theorem helps us confirm that if two angles and the included side of a triangle are the same in another triangle, then the two triangles are congruent using the AAS congruence rule!