a b c p q r

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

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

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

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.

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.

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

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

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 AC = DF  C =  F

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

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

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

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 = 90 o BC = EF AC = DF  B =  E  C =  F AB = DE

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

1.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