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GEOMETRY Congruent Triangles HELLO CLASS! • Students: Please watch this quick video before beginning this PowerPoint. Click the Picture Objectives for Today: At the end of this PowerPoint you should be able to • Accurately recognize that two not similar figures are not congruent • Identify corresponding parts of two congruent triangles with complete accuracy • Identify congruent triangles by SSS, SAS, ASA, or AAS theorems. • Identify which of the above theorems proves congruency. • Recognize that three congruent corresponding angles does not make triangles congruent. CONGRUENCY CHECKLIST • Figures are congruent if they are: • The same shape • The same size • All corresponding angles are congruent • All corresponding sides are congruent But what are corresponding angles and sides? CORRESPONDING ANGLES AND SIDES If ΔDEF was moved on top of ΔGHI, they would look like one triangle. Therefore, ∠D and ∠G are corresponding and EF and HI are corresponding sides. CORRESPONDING ANGLES AND SIDES Sometimes figures have to be rotated or mirrored to find corresponding angles and sides. ∠D and ∠A are corresponding angles DF and AB are corresponding sides THINGS THAT CANNOT BE CONGRUENT • Figures that are not the ºsame shape cannot be congruent. • Figures that are not the same size cannot be congruent. • If not all of the figure’s corresponding sides and angles are congruent, then the figures cannot be congruent. CONGRUENCY THEOREMS If all three sides of both triangles are congruent, the triangles are congruent. SIDE SIDE SIDE This is called the SSS theorem because: S S S ide GH = DE ide HI = EF ide FD = IG CONGRUENCY THEOREMS If two corresponding sides and an angle between them are equal between two triangles, the triangles are congruent. SIDE ANGLE SIDE This is called the SAS theorem because: S A S ide ngle ide GH = DE ∠G = ∠D GI = DF QUESTION ONE What angles are corresponding? ∠A and ∠E ∠E and ∠B I’m sorry… but your answer was not correct, please press this button to review this material. When you are done reviewing, press the button that looks like this to go back to the quiz. To Review CORRESPONDING ANGLES AND SIDES Sometimes figures have to be rotated or mirrored to find corresponding angles and sides. ∠D and ∠A are corresponding angles DF and AB are corresponding sides GOOD JOB!! You chose the correct answer. Continue QUESTION TWO Can these figures be congruent? No Yes I’m sorry… but your answer was not correct, please press this button to review this material. When you are done reviewing, press the button that looks like this to go back to the quiz. To Review THINGS THAT CANNOT BE CONGRUENT • Figures that are not the ºsame shape cannot be congruent. • Figures that are not the same size cannot be congruent. • If not all of the figure’s corresponding sides and angles are congruent, then the figures cannot be congruent. GOOD JOB!! You chose the correct answer. Continue QUESTION THREE Are these figures congruent? Yes No I’m sorry… but your answer was not correct, please press this button to review this material. When you are done reviewing, press the button that looks like this to go back to the quiz. To Review CONGRUENCY THEOREMS If all three sides of both triangles are congruent, the triangles are congruent. GOOD JOB!! You chose the correct answer. Continue ANGLE SIDE ANGLE THEOREM A S A ∠G = ∠D ngle ide ngle GI = DF ∠I = ∠F ANGLE ANGLE SIDE THEOREM A A S ngle ∠G = ∠D ngle ∠I = ∠F ide IH = FE AAA? THERE IS NO SUCH THING AS THE ANGLE ANGLE ANGLE THEOREM. This is why… Even though all of the angles are congruent, The figures obviously are not. A LITTLE EXTRA HELP • Here is a little song for you guys, hope you enjoy! • This website is great for extra explanation if you guys don’t quite understand. • Video on Youtube • Website QUESTION FOUR What theorem proves this congruency? SSA SAS I’m sorry… but your answer was not correct, please press this button to review this material. When you are done reviewing, press the button that looks like this to go back to the quiz. To Review SIDE ANGLE SIDE This is called the SAS theorem because: S A S ide ngle ide GH = DE ∠G = ∠D GI = DF GOOD JOB!! You chose the correct answer. Continue QUESTION FIVE Are these figures congruent? Yes No Maybe So I’m sorry… but your answer was not correct, please press this button to review this material. When you are done reviewing, press the button that looks like this to go back to the quiz. To Review AAA? THERE IS NO SUCH THING AS THE ANGLE ANGLE ANGLE THEOREM. This is why… Even though all of the angles are congruent, The figures obviously are not. You don’t know this for sure, if any one side is also congruent the figures are congruent. But you don’t know if a side is congruent or not. So, try again. Try Again GOOD JOB!! You chose the correct answer. Continue SUMMARY These all exist… • AAA does not!! THE END Thanks for watching, here is your homework assignment over this lesson. Please have it done by tomorrow Pg 365: Problem 12-50 evens