Congruent Triangle Proofs

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Using the Side-Side-Side Method to Prove Triangles Congruent

The SSS (Side-Side-Side) postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. The following figure illustrates [more…]

Using the Side-Angle-Side Method to Prove Triangles Congruent

The SAS (Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent [more…]

Using the Angle-Side-Angle Method to Prove Triangles Congruent

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent [more…]

Using the Isosceles Triangle Theorems to Solve Proofs

The following two theorems — If sides, then angles and If angles, then sides — are based on a simple idea about isosceles triangles that happens to work in both directions: [more…]

Using the Hypotenuse-Leg-Right Angle Method to Prove Triangles Congruent

The HLR (Hypotenuse-Leg-Right angle) theorem — often called the HL theorem — states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle [more…]

How to Do an Indirect Proof

Indirect proofs are sort of a weird uncle of regular proofs. With an indirect proof, instead of proving that something must be true, you prove it indirectly [more…]

Using Two Equidistant Points to Determine a Perpendicular Bisector

You can use two equidistant points to determine the perpendicular bisector of a segment. (To “determine” something means to fix or lock in its position, basically to show you where something is.) Here’s [more…]

Using a Point on a Perpendicular Bisector to Prove two Segments Congruent

You can use a point on a perpendicular bisector to prove that two segments are congruent. If the point is on the perpendicular bisector of a segment, then it’s equidistant from the endpoints of the segment [more…]

Using the Angle-Angle-Side Method to Prove Triangles Congruent

The AAS (Angle-Angle-Side) theorem states that if two angles and a nonincluded side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. The following [more…]

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