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# SAS, SSS, and ASA Postulates. Also Congruence Based on Coordinates.

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The concept I am learning today are SAS (side-angle-side), SSS (side-side-side), and ASA(angle-side-angle) postulates. I believe that i have a good understand of this, but I am having trouble with finding if a triangle is congruent based on two sets of coordinate points. I am asking for someone to explain this to me then give me a practice problem in order to check my understanding. Oct 2, 2018

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Example

Let   triangle ABC  have the following coordinates  ...A  = (0,0)  B  = (0, 3)  and C  = (4,0)

Let triangle DEF   have the following  coordinates ... D = (5,0)  E = (1,3)  F (1,0)

First calculate the distances between AB, AC  and BC

AB  =  sqrt  [ (0 - 0)^2 + (3 -0)^2 ] = sqrt  = 3

AC = sqrt [ (4 - 0)^2 + (0 -0)^2  ]  = sqrt [ 16]  = 4

BC = sqrt  [ (4 - 0)^2 + ( 3-0)^2 ]  = sqrt [ 16 +  9 ] = sqrt [25 ] = 5

Next calculate the distances between DE, DF and EF

DE  = sqrt [ (5 -1)^2 + (3 - 0)^2 ]  = sqrt [ 4^2 + 3^2 ] = sqrt [ 16 + 9 ] = sqrt   = 5

DF  = sqrt [ (5 - 1)^2  + ( 0 - 0)^2 ]= sqrt [ 4^2] = sqrt [ 16] =4

EF  = sqrt [ (1 - 1)^2 + (3 - 0)^2 ] = sqrt [ 3^2]  = sqrt  = 3

Since AB = EF  and AC = DF  and BC = DE

Then..by S-S-S   these triangles are congruent

I'll let you see if these are congruent...remember....the distances must "match" to have S-S-S  congruecy

triangle ABC  .... A  = (0,0)   B  = (0, 4)  C  = (3,0)

triangle DEF  ...D  = ( 1,0)    E  = (4, 0)   F  = (0, 5)   Oct 4, 2018