# Flashcards › Geometry Theorems and Postulates 7-10

## Postulate 7-1 (Angle-Angle Similarity [AA~]) If two angles of one triangle are congruent to the two angles of another triangle, then the triangles are similar. Theorem 7-1 (Side-Angle-Side Similarity [SAS~]) If an angle of one triangle is congruent to the angle of a second triangle, and the sides inculding the two angles are proportional, then the triangles are similar. Theorem 7-2 (Side-Side-Side Similarity [SSS~]) If the corresponding sides of two triangles are proportional, then the triangles are similar. Theorem 7-4 (Side-Splitter Theorem) If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Theorem 7-5 (Triangle-Angle-Bisector Theorem) If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. Theorem 8-1 (Pythagorean Theorem) a2 + b2 = c2 Theorem 8-2 (Converse of the Pythagorean Theorem) If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. Theorem 8-3 If c2 is greather than the sum of a2 and b2, then the triangle is obtuse. Theorem 8-4 If c2 is less than the sum of a2 and b2, then the triangle is acute. Theorem 8-5 (45-45-90 Triangle Theorem) In a 45-45-90 triangle, both the legs are congruent and x, and the hypotenuse is x(square root 2) Theorem 8-6 (30-60-90 Triangle Theorem) In a 30-60-90 triangle, the hypotenuse is 2x, the shorter leg is x, and the longer leg is x(square root 3) Theorem 10-1 (Area of a Rectangle) A=bh Theorem 10-2 (Area of a Parallelogram) A=bh Theorem 10-3 (Area of a Triangle) A=1/2bh Theorem 10-4 (Area of a Trapezoid) A=1/2h(b1 + b2) Theorem 10-5 (Area of a Rhombus or a Kite) A=1/2d1d2 Theorem 10-6 (Area of a Regular Polygon) A=1/2ap