ENGRTOMBA2018 wrote:
noTh1ng wrote:
What i don't get is why we can assume that the two triangles are similar just because AB = BC?
I mean i looks similar, but why can we apply that?
Refer to the attached figure for description of the points.
BD and CE are perpendicular to AE.
So, in triangles ABD and ACE, angle A is common angle to both the triangles, \(\angle{ADB} = \angle{AEC} = 90\) and \(\angle {ABD} = \angle{ACE}\) (BD || CE)
Thus triangles ABD ad ACE are similar by AA (or angle -angle similarity theorem)
Thus, by similarity
AB/ AC = BD / CE
Given BD = 5 and AB = 0.5*AC
Thus CE = 10. Hence, Statement 2 is sufficient.
Per statement 1, x =30 does not provide us any other useful information.
Thus B is the correct answer.
Hope this helps.
I continuously struggle with setting up the ratios for similar triangles.
SO would it be correct to say one ratio is you want to set it up in a way such that the ratio is between the CORRESPONDING sides? e.g.
AB = hypotenuse of smaller triangle, AC = hypotenuse of larger triangle
BD = leg of smaller triangle, CE = leg of larger triangle
AB/AC = BD/CE = k where k is some scale factor?
Would you ever set up the ratio between two sides of a triangle (e.g. the smaller triangle) and equate that with the ratio of the two sides of another triangle (e.g. the larger triangle)?
Second question is, how do we know that BD = 1/2 AB?
chetan2u and other experts, please chime in. I keep getting stuck on this over and over.
For example, I just added a document showing another problem. In that particular problem, the ratio was set up such that the ratio was between the sides of the SAME triangle and set equal to the ratio of the sides of the OTHER similar triangle. I am wondering what's the difference?
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