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In ∆ ABC above, which of the following must be true?

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In ∆ ABC above, which of the following must be true? [#permalink]

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New post 01 Sep 2017, 01:02
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In ∆ ABC above, which of the following must be true?

(A) r + s = x + y
(B) r + s = y – s
(C) r – s = x + y
(D) r – s = x – y
(E) r – s = y – x

[Reveal] Spoiler:
Attachment:
2017-09-01_1158.png
2017-09-01_1158.png [ 7.21 KiB | Viewed 570 times ]
[Reveal] Spoiler: OA

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Re: In ∆ ABC above, which of the following must be true? [#permalink]

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New post 01 Sep 2017, 01:18
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Bunuel wrote:
Image
In ∆ ABC above, which of the following must be true?

(A) r + s = x + y
(B) r + s = y – s
(C) r – s = x + y
(D) r – s = x – y
(E) r – s = y – x

[Reveal] Spoiler:
Attachment:
2017-09-01_1158.png


As per the given information in the above triangle, we can see that:

r + x = 90

s + y = 90

So let's equate both the equations.

r + x = s + y = 90

r + x = s + y

r - s = y - x

Hence E - (E) r – s = y – x
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Re: In ∆ ABC above, which of the following must be true? [#permalink]

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New post 07 Sep 2017, 07:14
Bunuel wrote:
Image
In ∆ ABC above, which of the following must be true?

(A) r + s = x + y
(B) r + s = y – s
(C) r – s = x + y
(D) r – s = x – y
(E) r – s = y – x

[Reveal] Spoiler:
Attachment:
2017-09-01_1158.png


We can create the following equation:

r + x + 90 = s + y + 90

r + x = s + y

r - s = y - x

Answer: E
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Re: In ∆ ABC above, which of the following must be true? [#permalink]

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New post 07 Sep 2017, 09:24
Bunuel wrote:
Image
In ∆ ABC above, which of the following must be true?

(A) r + s = x + y
(B) r + s = y – s
(C) r – s = x + y
(D) r – s = x – y
(E) r – s = y – x

[Reveal] Spoiler:
Attachment:
2017-09-01_1158.png


In the given triangles, r+x=90 and s+y=90, since the other angle is 90 in the triangles.
therefore, r+x=s+y
or r-s=y-x (E)
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Re: In ∆ ABC above, which of the following must be true? [#permalink]

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New post 07 Sep 2017, 10:08
Answer is E.


s+y+90=180
s+y=180-90

r+x=90

r+x=s+y
r-s=y-x

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Re: In ∆ ABC above, which of the following must be true?   [#permalink] 07 Sep 2017, 10:08
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