* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Congruent-Triangles
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
History of geometry wikipedia , lookup
Penrose tiling wikipedia , lookup
Noether's theorem wikipedia , lookup
Technical drawing wikipedia , lookup
Apollonian network wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euler angles wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
CONGRUENT TRIANGLES Congruence • We know… • Two SEGMENTS are congruent if they’re the same length. 2” 2” • Two ANGLES are congruent if they have the same measure. 60° 60° Third Angles Theorem • If two angles of one triangle are congruent to two angles of a second triangle, then: • The third angles are also congruent • The two triangles are SIMILAR (but not necessarily CONGRUENT) Triangle Congruence • Congruence: Two triangles are CONGRUENT if (and only if) they have three pairs of congruent sides and three pairs of congruent angles. Corresponding Parts • If two triangles are congruent, then: • The corresponding sides are the sides that are congruent • The corresponding angles are the angles that are congruent Minimum Information for Congruence • There are three angles and three sides to every triangle, so there are six pieces of information. • We need to know that at least THREE pieces of information match (with some restrictions). Theorem #1: SSS • If the side lengths of two triangles are congruent, then the triangles are congruent. Theorem #2: SAS • If two sides and the angle between them are congruent, then the triangles are congruent.