Unit 3 by Patrick
Triangle Sum Theorem- The sum of the angle measures of a triangle is 180°.
Corollary- The acute angles of a right triangle are always complementary. In triangle ABC, the two acute angles add up to 80°, and all of the angles add up to 180°. Exterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. In triangle ABC, angles A plus B equals the exterior measure of angle C. Third Angles Theorem- If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. Given <ADB congruent to <ACB, and <DAB congruent to <CAB, you can tell that <ABD congruent to <ABC. In the picture, they are both right angles, so it is easy to see. Isosceles Triangle Theorem- If two sides of a triangle are congruent, then the angles opposite the sides are congruent. In triangle ADC, AD is congruent to AC, so <ADB is congruent to <ACB. Converse of Isosceles Triangle Theorem- If two angles of a triangle are congruent, then the sides opposite those angles are congruent. In triangle ADC, <ADB is congruent to <ACB, so AD is congruent to AC. Equilateral Triangle Theorem- If a triangle is equilateral, then it is equiangular. In triangle ABC, it is equilateral, and as a consequence, it is also equiangular. Equiangular Triangle Theorem- If a triangle is equiangular, then it is equilateral. In triangle ABC, it is equiangular, and as a consequence, it is also equilateral. I chose these theorems and postulate because they are from the first lesson, and I have gotten to understand them better than most of the other postulates. Also, they seemed easy to put in a picture, not like some of the lesson 7 ones. |