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Types of Triangles

"Triangles can be classified by their angle measures and side lengths. For triangles only, equiangular and equilateral have the same implications: all sides and angles are congruent. Isosceles trian ...

Two Column Proofs

"Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "pro ...

Triangle Side and Angle Inequalities

"In any triangle, the largest angle is opposite the largest side (the opposite side of an angle is the side that does not form the angle). The shortest angle is opposite the shortest side. Therefore, ...

Triangle Inequality

"The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. To find a range of values for the third side when given two lengt ...

Triangle Angle Sum

"The sum of the three angles in any triangle sum to 180 degrees. The importance of this fact in Geometry cannot be emphasized enough. The triangle angle sum theorem is used in almost every missing a ...

Hypotenuse Leg

"In right triangles, if two legs are congruent and if the two hypotenuses are congruent, then the triangles are congruent. This is known as the hypotenuse leg theorem. Note that this is the SSA shortc ...

SSS and SAS

"When two triangles are congruent, all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent. If all three pairs of corresponding sides are congru ...

Flowchart Proofs

"Flowchart proofs are organized with boxes and arrows; each "statement" is inside the box and each "reason" is underneath each box. Each statement in a proof allows another subsequent statement to be ...

Similar Triangles in Circles and Right Triangles

"Two triangles in a circle are similar if two pairs of angles have the same intercepted arc. Sharing an intercepted arc means the inscribed angles are congruent. Since these angles are congruent, the ...

Remote Interior Angles

"If one side of a triangle is extended beyond the vertex, an exterior angle is formed. This exterior angle is supplementary with its adjacent, linear angle. Since the angle sum in a triangle is also 1 ...

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