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# Which of the following statements about the cube must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 51035
Which of the following statements about the cube must be true?  [#permalink]

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03 Jul 2018, 08:11
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:50) correct 12% (00:22) wrong based on 31 sessions

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Which of the following statements about the cube must be true?

I. Line 1-3 is parallel to Line 4-6
II. Triangle 3-4-7 has the same area as Triangle 1-6-8
III. Line 3-6 = Line 1-4

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Attachment:

set210.jpg [ 9.21 KiB | Viewed 324 times ]

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Re: Which of the following statements about the cube must be true?  [#permalink]

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03 Jul 2018, 08:14
Bunuel wrote:

Which of the following statements about the cube must be true?

I. Line 1-3 is parallel to Line 4-6
II. Triangle 3-4-7 has the same area as Triangle 1-6-8
III. Line 3-6 = Line 1-4

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Attachment:
set210.jpg

All are true since it is a cube, the answer must be (E)I, II, and III
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Re: Which of the following statements about the cube must be true?  [#permalink]

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03 Jul 2018, 22:33
Bunuel wrote:

Which of the following statements about the cube must be true?

I. Line 1-3 is parallel to Line 4-6
II. Triangle 3-4-7 has the same area as Triangle 1-6-8
III. Line 3-6 = Line 1-4

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Attachment:
The attachment set210.jpg is no longer available

Property:-
A cube has rotational axes of symmetry through the centers of a pair of opposite edges (two-fold symmetry, six axes), two opposite corners (three-fold symmetry, four axes), or the centers of two opposite faces (four-fold symmetry, three axes).

I. Line 1-3 is parallel to Line 4-6 (symmetry through the the centers of a pair of opposite edges)
II. Triangle 3-4-7 has the same area as Triangle 1-6-8 (symmetry through the centers of a pair of opposite edges)
III. Line 3-6 = Line 1-4 (symmetry through two opposite corners)

Diagram enclosed.

Ans. E
Attachments

File comment: The nine symmetry planes of the cube indicated by the dashed lines.

symmetry of planes.JPG [ 20.13 KiB | Viewed 248 times ]

Cube symmetry.JPG [ 35.22 KiB | Viewed 248 times ]

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Re: Which of the following statements about the cube must be true? &nbs [#permalink] 03 Jul 2018, 22:33
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