Two triangles can be proven congruent by SAS (Side-Angle-Side) if they have two sides and the included angle between them that are equal in both triangles.
For example, if triangle ABC and triangle DEF have the following measurements:
AB = DE BC = EF ∠BAC = ∠EDF
Then we can use SAS to prove that triangle ABC and triangle DEF are congruent.
It is important to note that the side between the two given sides must be the included angle, meaning that it must be the side that is in between the two given sides and angles. If this is not the case, then the triangles cannot be proven congruent using SAS.
Types of Triangle
Triangles can be classified based on their sides and angles. Here are the different types of triangles:
- Scalene Triangle: A scalene triangle is a triangle with all sides of different lengths. Also, none of the angles are equal.
- Isosceles Triangle: An isosceles triangle is a triangle with two sides of equal length. Also, the two angles opposite to the equal sides are equal.
- Equilateral Triangle: An equilateral triangle is a triangle with all three sides of equal length. Also, all three angles are equal, and each angle measures 60 degrees.
- Right Triangle: A right triangle is a triangle with one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs.
- Obtuse Triangle: An obtuse triangle is a triangle with one angle greater than 90 degrees.
- Acute Triangle: An acute triangle is a triangle with all three angles measuring less than 90 degrees.
These are the six types of triangles based on their sides and angles.