Question

1. match the correct answers.

gi ≅ jl, gh ≅ jk, and ∠g > ∠j

according to the hinge theorem:

a. hj
b. ∠l
c. ∠h
d. kl

Explanation:

Step1: Recall Hinge Theorem

The Hinge Theorem (also known as the SAS Inequality Theorem) states that if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Step2: Identify Corresponding Parts

We have \( GI \cong JL \) and \( GH \cong JK \). The included angles are \( \angle G \) (in \( \triangle GHI \)) and \( \angle J \) (in \( \triangle JKL \)) with \( \angle G>\angle J \). By the Hinge Theorem, the third side of \( \triangle GHI \) (which is \( HI \)) should be longer than the third side of \( \triangle JKL \) (which is \( KL \)). Also, for the angles, if we consider the converse or other parts, but in this case, matching the sides: the third side of the first triangle (with larger included angle) is \( HI \) and the third side of the second is \( KL \), and for angles, but here the first dropdown (left) and second (right). Wait, let's re - check:

Given \( GI \cong JL \), \( GH \cong JK \), \( \angle G>\angle J \). So in \( \triangle GHI \) and \( \triangle JKL \), two sides congruent, included angle of first is larger. So \( HI > KL \). So the left dropdown (first) should be \( HI \) (option a) and the right dropdown should be \( KL \) (option d), or if it's angle - side? Wait, maybe the first part is the side of the first triangle and the second is the side of the second. So according to Hinge Theorem, \( HI>KL \), so the first box (left) is \( HI \) (a) and the second (right) is \( KL \) (d). Also, if we consider angle - side, but the options are a. \( HI \), b. \( \angle L \), c. \( \angle H \), d. \( KL \).

So applying Hinge Theorem: \( GI \cong JL \), \( GH \cong JK \), \( \angle G>\angle J \implies HI > KL \). So the first dropdown (left) is \( HI \) (a) and the second (right) is \( KL \) (d).

Answer:

Left Dropdown: a. \( HI \), Right Dropdown: d. \( KL \)