Question

1. what could you prove about the following diagram, using the hinge theorem?

ij > jk
hi > hj
hk > hi
hj > hk

Explanation:

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second. In the diagram, the segments from H to the red marks are congruent (indicated by the red ticks), so the two triangles share a common pair of congruent sides. The included angle for side IJ is 34°, and for side JK is 31°. Since 34° > 31°, the third side opposite the larger angle (IJ) is longer than the third side opposite the smaller angle (JK).

Answer:

IJ > JK