DSQ: Calculating if two acute / obtuse triangles are similar - GMAT Quantitative
Card 1 of 16
Which of two triangles has greater area, 
or 
?
Statement 1: 
Statement 2: 
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that 
by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in 
to the corresponding side in 
, so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of 
to 
is 
, making 
the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
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True or false:
Statement 1: 
Statement 2: 
and 
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →
Which of two triangles has greater area, or ?
Statement 1:
Statement 2:
Which of two triangles has greater area,
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone proves that by the Angle-Angle Postulate, but does not prove anything about the sides, which would be needed to answer this question. Statement 2 alone only gives a relationship between one side of each triangle; without any further information, this is insufficient.
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in to the corresponding side in , so, as the triangles are similar, this ratio is shared by all three pairs of corresponding sides. Since
,
1.1 is this common ratio, and the ratio of the area of to is , making the larger triangle.
Statement 1 alone proves that
The two statements together, however, present sufficient evidence. Statement 1 proves that the triangles are similar. Statement 2 gives the ratio of one side in
1.1 is this common ratio, and the ratio of the area of
← Didn't Know|Knew It →
True or false:
Statement 1:
Statement 2: and
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
Statement 1 alone gives a proportion between two pairs of corresponding sides of the triangles. This is not enough to prove the triangles similar without the third side proportionality (SSS Simiilarity statement) or the congruence of the included angles (SAS Similarity statement).
Statement 2 gives two congruencies between corresponding angles, which by the Angle-Angle statement is enough to prove the triangles similar.
← Didn't Know|Knew It →