DSQ: Calculating whether acute / obtuse triangles are congruent - GMAT Quantitative

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.

If only one of the statements is known to be true, the only congruent pairs that are known between the triangles comprise two sides and a non-included angle; this information cannot prove congruence between the triangles. If both are known to be true, however, they, along with either of the given side congruences, set up the conditions for the Angle-Angle-Side Theorem, and the triangles can be proved congruent.

The answer is that both statements together are sufficient to answer the question, but not either alone.

We are given two triangles with two side congruences between them. If we compare their included angles (the angles that they form), the angle that is of greater measure will have the longer side opposite it. This is known as the Hinge Theorem.

The first statement says explicitly that the first included angle, , has greater measure than the second, , so the side opposite , , has greater measure than .

The second statement is not so explicit. But if is a right angle, must be acute, and if is right, then , which again proves that .

The answer is that either statement alone is sufficient to answer the question.