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Transcript
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 triangleright obtuse scalene equilateral acute isosceles 4-3 Angle Relationships in Triangles • auxiliary 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. 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 AC=BD CD=CD ACD= BDC *See slide 11 for SAS G G Reflexive 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 angle side angle- when the two angles and included side are angles 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 E CED is isos. AE=BE AEC=BED CE=ED AEC= BED AC=BD G G verticle Def. of isos SAS CPCTC 4-9 Isosceles and Equilateral Triangles Isosceles Triangles- a triangle with two sides congruent and the two corresponding angles are congruent A Try It Yourself! Given: AD bisects ABC, Prove: ABC is isosceles B C D Equilateral Triangle- a triangle with all sides and angles are congruent See, all sides and angles ARE congruent!
