Assume Statement 1 only. By the Pythagorean Theorem,, so; subsequently,, and one side congruence is proved. However, this, along with one angle congruence - the congruence of right anglesand- is not enough to prove or disprove triangle congruence.

Assume Statement 2 only. By the Pythagorean Theorem,. Since, it follows that, and, subsequently,. Since, if,, it follows by contradiction thatis a false statement.

Assume Statement 1 alone is true. Since each right triangle is inscribed inside a circle, each of the right angles is inscribed in that circle, and each intercepts a semicircle. That makes the two hypotenuses of the triangles,and, diameters; since they are on thesamecircle, their lengths are the same. However, no information is given about any of the other sides or angles, so no congruence can be proved or disproved.

Statement 2 alone gives us only congruence between one set of corresponding legs, which, along with one angle congruence, is insufficient to prove or to disprove triangler congruence.

Now assume both statements are true. From Statement 1, it follows that congruence of hypotenuses, and Statement 2 gives us congruence of corresponding legs; this sets up the conditions of the Hypotenuse-Leg Theorem, so it follows that.

Assume both statements are true. We show that both statements are insufficient to answer the question.

Supposeand.

and, satisfying the conditions of Statement 2.

The area of a right triangle is half the product of the lengths of its legs. Each triangle therefore has as its area, making the areas the same; Statement 1 is satisfied.

Since corresponding legs of the triangles are congruent,by the Side-Angle-Side Postulate.

Now, supposeand.

and, satisfying the conditions of Statement 2.

The area of a right triangle is half the product of the lengths of its legs. Each triangle therefore has as its area, making the areas the same; Statement 1 is satisfied.

However,and, so it is not true that.

Assume Statement 1 alone. The statement gives that all four legs of both triangles are congruent - specifically,and. Since the right angles are also congruent, then, by the Side-Angle-Side Postulate,.

Assume Statement 2 alone. The statement gives that all four acute angles are congruent - specifically, thatand. However, since we do not have any congruence or noncongruence between corresponding sides, congruence of the triangles cannot be proved or disproved.