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: Analyze $\triangle HIJ$

In $\triangle HIJ$, $HI = IJ$ (marked with equal signs), so it's isosceles. $\angle H = 70^\circ$, so $\angle IJH=\angle H = 70^\circ$ (base angles of isosceles triangle). Then $\angle I=180^\circ - 70^\circ - 70^\circ=40^\circ$.

Step2: Analyze $\triangle JKL$

In $\triangle JKL$, $JK = KL$ (marked with equal signs), so it's isosceles. $\angle K = 40^\circ$, so $\angle JKL$ has $\angle J=\angle L=(180^\circ - 40^\circ)/2 = 70^\circ$.

Step3: Check similarity

Now, in $\triangle HIJ$ and $\triangle JKL$: $\angle H = \angle J = 70^\circ$, $\angle I=\angle K = 40^\circ$, $\angle IJH=\angle L = 70^\circ$? Wait, no, re - check: $\triangle HIJ$ angles: $\angle H = 70^\circ$, $\angle I = 40^\circ$, $\angle IJH=70^\circ$. $\triangle JKL$ angles: $\angle K = 40^\circ$, $\angle J=\angle L = 70^\circ$. So corresponding angles are equal: $\angle H=\angle J$, $\angle I=\angle K$, $\angle IJH=\angle L$. By AA (Angle - Angle) similarity criterion, the triangles are similar.

Answer:

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