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605-655 (Medium)|   Geometry|      
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The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC 12 Nov 2019, 00:39
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[GMAT math practice question]

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(geometry) The triangle \(ABC\) is the equilateral triangle. Moreover, \(AB, BC\), and \(AC\) are parallel to \(n, l,\) and \(m,\) respectively. As the figure shows, \(DI = 3, EF = 2, FG = 6\) and \(HG = 1.\) What is \(x + y\)?

A. \(6\)

B. \(7\)

C. \(8\)

D. \(9\)

E. \(10\)
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D
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The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC 14 Nov 2019, 01:26
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Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D
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The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC 31 Aug 2022, 06:26
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MathRevolution
=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D
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Hey, why are triangles ADI, BEF, CGH equilateral triangles?
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The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC 19 Sep 2022, 12:34
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Blair15
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=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D


Hey, why are triangles ADI, BEF, CGH equilateral triangles?
Show more

Blair15
Consider triangle ADI and triangle ABC
Angle A is common in both triangles
Since DI is || BC, angle B= angle D and angle C= angle (corresponding angles)
Since all three angles are same, the two triangles are similar.
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The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC 19 Sep 2022, 12:45
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asterisk357
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MathRevolution
=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D


Hey, why are triangles ADI, BEF, CGH equilateral triangles?

Blair15
Consider triangle ADI and triangle ABC
Angle A is common in both triangles
Since DI is || BC, angle B= angle D and angle C= angle (corresponding angles)
Since all three angles are same, the two triangles are similar.
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So if a triangle is similar to an equilateral triangle, it makes the other triangle equilateral too?
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The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC 19 Sep 2022, 13:16
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Hey, why are triangles ADI, BEF, CGH equilateral triangles?[/quote]

Blair15
Consider triangle ADI and triangle ABC
Angle A is common in both triangles
Since DI is || BC, angle B= angle D and angle C= angle (corresponding angles)
Since all three angles are same, the two triangles are similar.[/quote]

So if a triangle is similar to an equilateral triangle, it makes the other triangle equilateral too?[/quote]

Yes. The ratio of the corresponding sides are equal.
[Refer attachment]
Assume if the triangles are equilateral.
Assuming AB=5, then BC=5
5/DE=5/EF=5/DF
DE=EF=DF

Apply same method to this question
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