Geometry Theorems/Postulates/Corollaries

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Theorem 4.1

Angle Sum Theorem- The sum of the measures of the angles of a triangle is 180 degrees

Theorem 4.2

Third Angle Theorem- If two angles of one triangle are congruent to tow angles of a second triangle, then the third angles of the triangles are congruent.

Theorem 4.3

Exterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Corollary 4.1

The acute angles of a right triangle are complementary.

Corollary 4.2

There can be at most one right or obtuse angle in a triangle.

Theorem 4.4

Congruence of triangles is reflexive, symmetric, and transitive.

Postulate 4.1

Side-Side-Side Congruence (SSS)- If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

Postulate 4.2

Side-Angle-Side Congruence (SAS)- 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.

Postulate 4.3

Angle-Side-Angle Congruence (ASA)- If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

Theorem 4.5

Angle-Angle-Side Congruence (AAS)- If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.

Theorem 4.6

Leg-Leg Congruence (LL)- If the legs of one right triangle are congruent to the corresponding legs of another right angle, then the triangles are congruent.

Theorem 4.7

Hypotenuse-Angle Congruence (HA) If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, the the two triangles are congruent.

Theorem 4.8

Leg-Angle Congruence (LA) - If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

Postulate 4.4

Hypotenuse-Leg Congruence (HL)- If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

Theorem 4.9

Isosceles Triangle Theorem- If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Theorem 4.10

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Corollary 4.3

A triangle is equilateral if and only if it is equiangular

Corollary 4.4

Each angle of an equilateral triangle measures 60 degrees.

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