Triangle Congruence Theorems

Note: The order of the angles (or sides) matters. If the theorem is ASA you have to have a side in between two angles.​

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​SSS: If two triangles have 3 congruent sides then the triangles are congruent.

​SAS: Side Angle Side

ASA: Angle Side Angle

​AAS: Angle Angle Side

HL: When comparing two right triangles, if they share a leg and a hypotenuse in common they are congruent.​

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​Ex: What theorem proves the triangles are congruent?

​A. What theorem proves these two triangles are congruent?

​B. Prove the two triangles are congruent.

Types of Triangles

Isosceles Triangles: Isosceles triangles have one pair of congruent sides and one pair of congruent angles.

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​Equilateral Triangles: Equilateral triangles are triangles with all sides and angles congruent.​

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​Ex: Solve for B

​If angle C is 30 degrees, find the measure of the other angles.

​If AC is 30 and CB is 10y and AB is 5x, solve for x and y.