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# Triangle Similarity

-1
250
3
+2448

I put what I think each of these are but I only think that I got a few of them right.

Feb 27, 2018

#1
+101870
+1

15...if these are similar....we must have that

13/15  =  30/35

13/15  = 6/7      not true....so these are not similar

16.....if these were similar.....we must have that

40/60  = 23/34

2/3  =  23/34  ....not true.....so.....not similar

17  For these to be similar...we must have that

16/22  = 25 /33

8/11  = 26/33      .....not true....not similar

18 EFG  similar to EBC

Angle E  = Angle E  and

EF / EG  = EB/EC

50/60  = 20/24

5/6  = 5/6

19 Not similar

20 Not similar

Feb 27, 2018
#2
+2448
-1

Ty, but are you sure they are all not similar (16,17,19,20)

Feb 27, 2018
#3
+101870
+2

One way for triangles to be similar is that we need that the ratios of the corresponding sides to be =

That is

short side of first triangle

_____________________        =  A

short side of second triangle

Intermediate side of first triangle

__________________________        =  B

Intermediate side of second triangle

Long side of first triangle

_______________________     =   C

Long side of second triangle

So  A = B  = C   for the triangles to be similar

So.....For 16 to be similar...we need that

23/40  = 34/55  = 36/60

23/40 = 34/55 = 3/5

None of these ratios are equal...so....not similar

For 17  to be similar....we need the sides around the equal angle need to be equal ratios

But

16/22   =  25/33  ???

8/11 = 25/33     these are not equal

For the same reason....the triangles in 19 aren't similar, either

In other words  14/9  not equal to 7/4

And the triangles in 20 are not similar because  we can't establish any AA similarity

Feb 27, 2018