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# ABC and PQR are both triangles. Is the area of triangle ABC

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ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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05 Feb 2012, 23:37
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ABC and PQR are both triangles. Is the area of triangle ABC greater than the area of triangle PQR?

(1) Sides AB=PQ, BC=QR, and AC=PR
( 2) Angles A=P, B=Q, and C=R
[Reveal] Spoiler: OA

Last edited by nafishasan60 on 06 Feb 2012, 01:27, edited 1 time in total.

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Re: ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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06 Feb 2012, 01:09
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ABC and PQR are both triangles. Is the area of triangle ABC greater than the area of triangle PQR?

(1) Sides AB=PQ, BC=QR, and AC=PR --> if three pairs of sides of two triangles are equal in length, then the triangles are congruent, they have the same shape and size. (Side-Side-Side case). So the area of triangle ABC is equal to that of the area of triangle PQR. Sufficient.

( 2) Angles A=P, B=Q, and C=R --> triangle ABC and triangle PQR are similar, but we need to know the lengths of the sides to answer the question. Not sufficient.

For more or congruent and similar triangles check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
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Re: ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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05 Aug 2013, 17:56
from 1
ABC is congruent to PQR.
areas equal.
sufficient to tell that area of ABC is NOT greater than PQR

from 2
ABC is similar to PQR.
area of ABC may be <, > or = to PQR.

hence A.

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Re: ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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05 Aug 2013, 23:25
nafishasan60 wrote:
ABC and PQR are both triangles. Is the area of triangle ABC greater than the area of triangle PQR?

(1) Sides AB=PQ, BC=QR, and AC=PR
( 2) Angles A=P, B=Q, and C=R

st(1), three sides are equal, so the base and height of the two triangles are same, consequently the areas are same.
st(2), triangles are similar, nothing we can be sure about the length of the triangles. so not sufficient.
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Re: ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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20 Feb 2014, 06:41
Bunuel wrote:
ABC and PQR are both triangles. Is the area of triangle ABC greater than the area of triangle PQR?

(1) Sides AB=PQ, BC=QR, and AC=PR --> if three pairs of sides of two triangles are equal in length, then the triangles are congruent, they have the same shape and size. (Side-Side-Side case). So the area of triangle ABC is equal to that of the area of triangle PQR. Sufficient.

( 2) Angles A=P, B=Q, and C=R --> triangle ABC and triangle PQR are similar, but we need to know the lengths of the sides to answer the question. Not sufficient.

For more or congruent and similar triangles check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.

They caught me on this one. Doesn't 1 depend on the way the sides are positioned?

Thanks
Cheers
J

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Re: ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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20 Feb 2014, 07:49
jlgdr wrote:
Bunuel wrote:
ABC and PQR are both triangles. Is the area of triangle ABC greater than the area of triangle PQR?

(1) Sides AB=PQ, BC=QR, and AC=PR --> if three pairs of sides of two triangles are equal in length, then the triangles are congruent, they have the same shape and size. (Side-Side-Side case). So the area of triangle ABC is equal to that of the area of triangle PQR. Sufficient.

( 2) Angles A=P, B=Q, and C=R --> triangle ABC and triangle PQR are similar, but we need to know the lengths of the sides to answer the question. Not sufficient.

For more or congruent and similar triangles check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.

They caught me on this one. Doesn't 1 depend on the way the sides are positioned?

Thanks
Cheers
J

Actually, no. Any two triangles with three equal sides are basically the same, congruent.
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Re: ABC and PQR are both triangles. Is the area of triangle ABC [#permalink]

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27 Jun 2016, 10:55
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Re: ABC and PQR are both triangles. Is the area of triangle ABC   [#permalink] 27 Jun 2016, 10:55
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