to Results Date (5/4/04) Congruent Triangles
(the following were gone over in class on 4/27): Theorem 1 (SAS) If 2 sides and the included angle of a one triangle are equal, respectively, to those of a second triangle, then the two triangles are congruent. Theorem 2 If two sides of a triangle are equal then the angles opposite them are also equal. Theorem 3 (SSS) If three sides of one triangle are equal, respectively, to three sides of a second triangle, then the two triangles are congruent. Theorem 4 (ASA) If an angle, a side, and an angle are respectively equal to an angle, side and angle of a second triangle then the two triangles are congruent.
Measures of Angles:
(the following come from the fist homework assignment): Theorem 5A If two straight lines intersect then the vertical angles are equal (felt by some people to be necessary prior to the proof of Theorem 5) Theorem 5 Two parallel lines are cut by a transversal if and only if the alternate-interior angles are equal. (2 theorems 2 problems) Theorem 6 The sum of the angles of triangle a is equal to a straight angle. Theorem 7 The sum of the angles in a quadrilateral equal 2 straight angles Theorem 8 (added on May 5) If a line is perpendicular to one of two parallel lines then it is parallel to the other
Parallelograms
Theorem 9 The opposite sides of a parallelogram are equal Theorem 10 The diagonals of a parallelogram bisect each other
Area
Theorem 11 The area of a right triangle is half of the length of the base times the height Theorem 12 The area of any triangle is half of the length of the base times the height
Theorem 13 The area of a parallelogram is the base times the height Theorem ...