Question

question 14 of 25

based on the information marked in the diagram, \\(\delta fgh\\) and \\(\delta jkl\\) must be congruent.

a. true
b. false

Explanation:

Identify the marked geometric information

We observe the markings on \(\triangle FGH\) and \(\triangle JKL\):

• Side \(GF\) has a single tick mark, and side \(KJ\) has a single tick mark, so \(GF \cong KJ\).
• Side \(FH\) has a double tick mark, and side \(JL\) has a double tick mark, so \(FH \cong JL\).
• \(\angle F\) and \(\angle J\) are marked as right angles, so \(\angle F \cong \angle J = 90^\circ\).

Analyze the congruence criteria

Using the Triangle Congruence Postulates, we have two pairs of congruent corresponding sides and a congruent included angle:

• Side: \(GF \cong KJ\)
• Included Angle: \(\angle F \cong \angle J\)
• Side: \(FH \cong JL\)

This configuration corresponds to the Side-Angle-Side (SAS) congruence postulate.

Determine the truth value

Since the SAS postulate is a valid criterion for triangle congruence, the two triangles must be congruent. Therefore, the statement is true.

Answer:

• A. True (Correct answer)
• B. False