Question

triangle congruence: asa and aas
analyzing diagrams
can you conclude that triangle ghf is congruent to triangle gjk? explain.
not enough information given
yes, by aas
yes, by asa
yes, by aaa

Explanation:

Step1: Identify right angles

$\angle GHF$ and $\angle GJK$ are right angles (marked with red squares), so $\angle GHF = \angle GJK = 90^\circ$.

Step2: Identify equal sides

$GH = GJ$ (marked with the same tick mark), so these sides are congruent.

Step3: Identify vertical angles

$\angle FGH$ and $\angle KGJ$ are vertical angles, so $\angle FGH = \angle KGJ$.

Step4: Apply ASA congruence

In $\triangle GHF$ and $\triangle GJK$:

• $\angle GHF = \angle GJK$ (right angles)
• $GH = GJ$ (given)
• $\angle FGH = \angle KGJ$ (vertical angles)

By the Angle - Side - Angle (ASA) congruence criterion, $\triangle GHF \cong \triangle GJK$.

Answer:

yes, by ASA