If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. ![]() The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.Įach leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. In a triangle, the largest angle is across from the longest side. In a triangle, the longest side is across from the largest angle. The sum of the lengths of any two sides of a triangle must be greater than the third side The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. If two triangles are similar, the corresponding sides are in proportion. If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent.Ĭorresponding parts of congruent triangles are congruent. Hypotenuse-Leg (HL) Congruence (right triangle) If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Triangles: Side-Side-Side (SSS) Congruence If two angles of a triangle are congruent, the sides opposite these angles are congruent. If two sides of a triangle are congruent, the angles opposite these sides are congruent. The measure of an exterior angle of a triangle is greater than either non-adjacent interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. The sum of the interior angles of a triangle is 180º. If two angles form a linear pair, they are supplementary. Supplements of the same angle, or congruent angles, are congruent.Ĭomplements of the same angle, or congruent angles, are congruent. ![]() The whole is equal to the sum of its parts.Īngle Addition Postulate: m ![]() If equal quantities are subtracted from equal quantities, the differences are equal. If equal quantities are added to equal quantities, the sums are equal. General: Reflexive PropertyĪ quantity is congruent (equal) to itself. You need to have a thorough understanding of these items. This is a partial listing of the more popular theorems, postulates and properties needed when working with Euclidean proofs.
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