Question

△hij and △jkl are shown below. which statement is true? △hij is similar to △jkl. △hij is not similar to △jkl. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find angle I in $\triangle HIJ$

In $\triangle HIJ$, using the angle - sum property of a triangle ($\angle H+\angle I+\angle J = 180^{\circ}$), given $\angle H = 70^{\circ}$ and since $\triangle HIJ$ is isosceles (two equal - side markings), $\angle J=\angle H = 70^{\circ}$. Then $\angle I=180^{\circ}-70^{\circ}-70^{\circ}=40^{\circ}$.

Step2: Compare angles of the two triangles

In $\triangle HIJ$ and $\triangle JKL$, $\angle I = \angle K = 40^{\circ}$, and the ratio of the sides between the equal angles can be considered. Also, the base - angle relationships and side - length relationships (from the equal - side markings) show that the two triangles are similar by the AA (angle - angle) similarity criterion.

Answer:

$\triangle HIJ$ is similar to $\triangle JKL$.