* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry 2.5 ‐ Proving Angles Congruent A. Recall: • Theorem ‐ a
Survey
Document related concepts
Topological quantum field theory wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of geometry wikipedia , lookup
Atiyah–Singer index theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Noether's theorem wikipedia , lookup
Riemann–Roch theorem wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Transcript
Geometry 2.5 ‐ Proving Angles Congruent A. Recall: Theorem ‐ a statement or theory that was proven to be true. The • process through which a theory is proven to be a theorem is called a proof Postulate ‐ a statement that is accepted as true but hasn’t been proven • true, thus hasn’t become a theorem. B. • Vertical Angles Theorem Vertical angles are congruent. 1 2 Sep 1711:01 AM 1 (2x ‐ 38)0 (2x ‐ 10)0 (4x ‐ 40)0 (x + 22)0 Sep 1711:04 AM 2 B (x + 81)0 C E C (y)0 (5x + 17) 0 (2x)0 D A (y + x)0 E B (y ‐ x)0 D A Sep 1711:04 AM 3 D. Congruent Complements Theorems Theorem 2.3 ‐ if two angles are complements of the same angle, or of congruent angles, then the two angles are congruent Theorem 2.4 ‐ all right angles are congruent Theorem 2.5 ‐ if two angles are congruent and supplementary, then each is a right angle. Sep 1711:05 AM 4 1 3 2 Sep 1711:07 AM 5 1 2 3 Sep 1711:08 AM 6 2.5 HW p. 112 #s 1 ‐ 13 all Sep 1711:08 AM 7