To determine if the two triangles are congruent, Malik can use the concept of HL (Hypotenuse-Leg) congruence for right triangles, which states that if two right triangles have equal lengths of the hypotenuse and one corresponding leg, then the triangles are congruent.
In this case, both triangles have a hypotenuse of 13 units. The first triangle has a leg of 12 units, while the second triangle has a leg of 5 units. To accurately assess the congruence, he would need to find the lengths of the missing legs of each triangle.
For the first triangle (leg = 12, hypotenuse = 13): Using the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] where \(c\) is the hypotenuse (13) and \(a\) is one leg (12): \[ 12^2 + b^2 = 13^2 \ 144 + b^2 = 169 \ b^2 = 169 - 144 \ b^2 = 25 \ b = 5 \] Therefore, for the first triangle, the sides are 5, 12, and 13.
For the second triangle (leg = 5, hypotenuse = 13): Using the Pythagorean theorem again: \[ a^2 + 5^2 = 13^2 \ a^2 + 25 = 169 \ a^2 = 169 - 25 \ a^2 = 144 \ a = 12 \] For the second triangle, the sides are also 5, 12, and 13.
Since both triangles have the same dimensions (5, 12, and 13), Malik can conclude that the triangles are congruent. Therefore, the best response is:
He could apply the concept of HL and show that the two triangles are congruent.
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