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.

OwenT154
Oct 2, 2018

#1**+2 **

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 [9] = 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 [25] = 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 [9] = 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)

CPhill
Oct 4, 2018