* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Triangle Congruence Tests 4.4 Proving Congruence
Survey
Document related concepts
Steinitz's theorem wikipedia , lookup
Penrose tiling wikipedia , lookup
Golden ratio wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Technical drawing wikipedia , lookup
Noether's theorem wikipedia , lookup
Euler angles wikipedia , lookup
History of geometry wikipedia , lookup
Four color theorem wikipedia , lookup
Apollonian network wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Reuleaux triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Advanced Geometry Triangle Congruence Lesson 2 Proving Triangles Congruent For two triangles to be congruent 6 pairs of parts must be congruent. The triangle congruence postulates and theorem allow us to prove two triangles are congruent using only 3 pairs of parts. Side-Side-Side Congruence Postulate p. 226 If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Side-Angle-Side Congruence Postulate p. 227 If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Angle-Side-Angle Congruence Postulate p. 235 If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-Angle-Side Congruence Theorem p. 236 If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. These are the tests that work: These tests DO NOT work: SSS AAA SAS SSA ASA AAS Examples: Determine which postulate or theorem can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. SAS Congruence Postulate ASA Congruence Postulate not possible AAS Congruence Theorem Examples: Determine whetherEFG MNP given the coordinates of the vertices. Explain. E 4, 3 , F 2,1 , G 2, 3 , M 4, 3 , N 2,1 , P 2, 3 Write a two-column proof. If AD DC and B is the midpoint of AC , then ABD CBD. Write a two-column proof. If K M and JK NM , then J N. Summary • Prove 3 pairs of parts congruent. – Use any reason we have learned. • Prove the triangles congruent. – Use a congruence test. • If necessary, prove a pair of parts congruent. – Use CPCTC.