using the information provided, select the triangle congruence criterion that can best be used to prove that $\delta hfg \cong \delta hkj$.

a. angle-angle-side (aas)
b. angle-side-angle (asa)
c. side-angle-side (sas)
d. side-side-angle (ssa)

Question

using the information provided, select the triangle congruence criterion that can best be used to prove that $\delta hfg \cong \delta hkj$.

a. angle-angle-side (aas)
b. angle-side-angle (asa)
c. side-angle-side (sas)
d. side-side-angle (ssa)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertical Angles", "Triangle Congruence Postulates" ], "new_concepts": [], "current_concepts": [ "Vertical Angles", "Triangle Congruence Postulates" ] } ## Identify given geometric markings $$ \begin{aligned} &\overline{FH} \cong \overline{KH} \quad \text{(indicated by single tick marks)} \ &\angle F \cong \angle K \quad \text{(indicated by single arc marks)} \end{aligned} $$ ## Identify vertical angles $$ \angle FHG \cong \angle KHJ \quad \text{(vertical angles theorem)} $$ ## Determine the congruence criterion $$ \begin{aligned} &\text{Two angles and the included side of } \Delta HFG \text{ are congruent to two angles and the included side of } \Delta HKJ. \ &\text{Criterion: Angle-Side-Angle (ASA)} \end{aligned} $$

A. angle-angle-side (AAS)

B. angle-side-angle (ASA)

C. side-angle-side (SAS)

D. side-side-angle (SSA)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Postulates" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given geometric markings

Identify vertical angles

Determine the congruence criterion

Answer: