Question
I will rate lifesaver. Given the figures, state whether the triangles are congruentbased upon the given conditions. If your answer is yes, namethe theorem or postulate abbreviation to justify your answer (Hint:Side, Angle, Side) _ _ __ <A=<E;<B=<D;A B=ED_________ __ __ __ BC= D F; <=<F;<and<E are rightangles_______ __ __ ___ __ __ __ __ A C= EF ;<C=<F; B C= D F ______ __ ___ __ __ ____ __ __ __ __ ___ A C = E F; B C = D F ; A B = ED _________
Explanation / Answer
1) AAS (angle angle side) (the third angle MUST be the samethough not given because the angles in a triangle add to 180 andsince one of the sides is the same, all three sides will be thesame) 2) Some information is missing where you have [ <=<F ] and[ <and<E are right angles ] 3) SAS (side angle side) (the third length {BA and DE} must bethe same because the two lines that span the angles <C and <Fare the same length meaning the line in between points {B and A}and {D and E} must be the same) 4) SSS (side side side) (because the three lines are of the samelength the angles between them will NEVER change they are fixedfrom the length of the three sides of the triangle. Meaning if youwere you increase the length of (for example) AC and BC then thatmeans EF and DF increase exactly the same because the condition isAC=EF and BC=DF. Hence the angle will neither increase ordecrease)