TRIANGLE CONGRUENCE p q r a b c LESSON 17

EXPLORING CONGRUENT TRIANGLES Goal 1: How to identify congruent triangles. Goal 2: How to identify different types of triangles . Definition of Congruent Triangles If ABC is congruent to PQR, then there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent. The notation ABC  PQR indicates the congruence. a b c p q r

at least two congruent sides Classification of Triangles By Sides isosceles triangle at least two congruent sides scalene triangle no congruent sides equilateral triangle three congruent sides

three congruent angles Classification of Triangles By Angles obtuse triangle one obtuse angle acute triangle three acute angles Equiangular three congruent angles right triangle one right angle

Congruence Again The congruence symbol ““ has a different meaning than the equal symbol “=“. In geometry “=“ means “identical to” or “exactly the same as,” but ““ means that the measure (a number value) of two distinct objects of the same class is the same, or that the measure of the corresponding parts of the two objects is the same.

CONGRUENT POSTULATES RECALL: Congruent triangles have 3 pairs of  angles and 3 pairs of  sides. Do we want to show that all three pairs of angles are congruent and that all three pairs of sides are congruent every time? YES!!! You can construct congruent triangles with a minimum amount of information using the congruent postulates.

CONGRUENT POSTULATES: SSS Side-Side-Side (SSS) Postulate: If all three pairs of corresponding sides of two triangles are equal, the two triangles are congruent. If you know: then you know: and you know: AB = DE BC = EF AC = DF A =  D B =  E C =  F

CONGRUENT POSTULATES: SSS Side-Side-Side (SSS) Postulate: AB = DE BC = EF AC = DF A =  D B =  E C =  F

CONGRUENT POSTULATES: SAS Side-Angle-Side (SAS) Postulate: If two pairs of corresponding sides and the corresponding contained angles of two triangles are equal, the two triangles are congruent. If you know: then you know: and you know: AB = DE  B =  E AC = DF A =  D BC = EF C =  F

CONGRUENT POSTULATES: SAS Side-Angle-Side (SAS) Postulate: A =  D BC = EF C =  F AB = DE  B =  E AC = DF

CONGRUENT POSTULATES: ASA Angle-Side-Angle (ASA) Postulate: If two angles and the contained side of one triangle are equal to two angles and the contained side of another triangle, the two triangles are congruent. If you know: then you know: and you know:  A =  D  B =  E AB = DE AC = DF C =  F BC = EF

CONGRUENT POSTULATES: ASA Angle-Side-Angle (ASA) Postulate:  A =  D  B =  E AB = DE AC = DF C =  F BC = EF

CONGRUENT POSTULATES: RHS Right angle - Hypotenuse-Side (RHS) Postulate: If the hypotenuse and another side of one right triangle are equal to the hypotenuse and one side of a second right triangle, the two triangles are congruent. If you know: then you know: and you know:  A =  D = 90o BC = EF AC = DF B =  E C =  F AB = DE

CONGRUENT POSTULATES: RHS Right angle - Hypotenuse-Side (RHS) Postulate:  A =  D = 90o BC = EF AC = DF B =  E C =  F AB = DE

PROPERTIES OF CONGRUENT TRIANGLES REFLEXIVE Every triangle is congruent to itself. 2. SYMMETRIC If ABC  PQR, then PQR  ABC 3. TRANSITIVE If ABC  PQR and PQR  TUV, then ABC  TUV

CLASS WORK Check solutions to lesson 16(3) Copy notes from Lesson 17 Do Lesson 17 worksheet