Chapter 4 Triangle Congruence By: Emily Gorges, Janie Eyerman, Andie Jamison, and Maria Ong

4-1 Congruence and Transformations Vocab:  dilation-changes size, not shape of a coordinate figure  reflection- a figure reflected over a line  translation- the same figure moved to another place on coordinate grid  rotation- a figure rotated around a vertex to a certain degree

4-2 Classifying Triangles Terms:  Right  Obtuse  Acute  Scalene  Equilateral  Isosceles  Equiangular

Example  Classify each triangle- right obtuse acute right obtuse acute scalene equilateral isosceles scalene equilateral isosceles

4-3 Angle Relationships in Triangles auxiliary line- a line that is added to a figure to aid in a proofauxiliary line- a line that is added to a figure to aid in a proof

Exterior Angle Theorem  The measure of the exterior angle of a triangle is equal to the sum of its remote interior angles.

Third Angle Theorem If two angles of a triangle are congruent to angles of another triangle then the third angles of both triangles are congruent. If two angles of a triangle are congruent to angles of another triangle then the third angles of both triangles are congruent.

4-4 Congruent Triangles Terms:  corresponding angles  corresponding sides  congruent polygons  overlapping triangles

Proof example Given: <ACD=<BDC, AC=BD Prove: ACD= BDC <ACD=<BDC G AC=BD G CD=CD Reflexive ACD= BDC SAS* *See slide 11 for SAS

4-5 Triangle Congruence: SSS and SAS Terms  included angle- the angle in between the 2 given sides  side side side- if all 3 sides of a triangle are congruent to the other triangle, then both triangles are congruent  side angle side- the two sides and the included angle are congruent to the other triangle, then both triangles are congruent

4-6 Triangle Congruence: ASA, AAS, and HL  included side- side between the 2 given angles  angle side angle- when the two angles and included side are congruent to the other triangle, then both triangles are congruent  angle angle side- when two angles and a not included side are congruent to the other triangle, then both triangles are congruent  hypotenuse leg- in right triangles when the hypotenuse and one leg are congruent to the other triangle, then both triangles are congruent

4-7 Triangle Congruence: CPCTC Given: CED is isosceles, AE=BE Prove: AC=BD CED is isos. G AE=BE G AEC=BED verticle CE=ED Def. of isos AEC= BED SAS AC=BD CPCTC E

4-9 Isosceles and Equilateral Triangles Isosceles Triangles- a triangle with two sides congruent and the two corresponding angles are congruent Given: AD bisects ABC, Prove: ABC is isosceles A CB D Try It Yourself!

Equilateral Triangle- a triangle with all sides and angles are congruent See, all sides and angles ARE congruent!