Question

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

Explanation:

Step1: Analyze ∠DEF and ∠JKL

Both ∠DEF and ∠JKL are right angles, so \( \angle DEF = \angle JKL = 90^\circ \).

Step2: Find ∠D in △DEF

In △DEF, the sum of angles in a triangle is \( 180^\circ \). So \( \angle D = 180^\circ - 90^\circ - 35^\circ = 55^\circ \).

Step3: Compare angles of the two triangles

In △JKL, \( \angle J = 55^\circ \), so \( \angle D = \angle J = 55^\circ \), and \( \angle DEF = \angle JKL = 90^\circ \). By AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. So △DEF ~ △JKL.

Answer:

\(\triangle DEF\) is similar to \(\triangle JKL\).