Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?The figure shows an isosceles triangle with an altitude drawn from the top vertex to the lower side. The left and right sides are each marked with 1 tick mark. The altitude is shown to meet the lower side at a right angle.
(1 point)
Responses
SAS
SAS
HL
HL
ASA
ASA
none
none
Skip to navigation
SAS is the criteria for triangle congruence that allows you to immediately conclude that the triangles are congruent without any extra steps.
The criteria for triangle congruence that allows you to immediately conclude that the triangles are congruent without any extra steps is HL (Hypotenuse-Leg).
In order to determine which criteria for triangle congruence allows us to immediately conclude that the triangles are congruent without any extra steps, we need to consider the given information.
From the figure, we can see that we have an isosceles triangle with an altitude drawn from the top vertex to the lower side. The left and right sides are each marked with one tick mark and the altitude meets the lower side at a right angle.
The given information implies that the triangles are right triangles, specifically right isosceles triangles since the altitude forms a right angle with the lower side, and the left and right sides are of equal length (since they each have one tick mark).
With this information, we can determine that the criteria for triangle congruence that allows us to immediately conclude that the triangles are congruent without any extra steps is HL (Hypotenuse-Leg). HL states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
In this case, the hypotenuse of both triangles is the side opposite the right angle, and the shared leg is the side formed by the altitude. Since the hypotenuse and one leg of the two right isosceles triangles are congruent, we can immediately conclude that the triangles are congruent using the HL criterion.