in the figure shown, $\overline{ps} \cong \overline{rq}$. which theorem can bs used to prove $\delta sqr \cong \delta qsp$?

a. sss congruence theorem
b. sas congruence theorem
c. aas congruence theorem
d. hl congruence theorem

Question

in the figure shown, $\overline{ps} \cong \overline{rq}$. which theorem can bs used to prove $\delta sqr \cong \delta qsp$?

a. sss congruence theorem
b. sas congruence theorem
c. aas congruence theorem
d. hl congruence theorem

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence Postulates" ], "new_concepts": [ "HL Congruence Theorem" ], "current_concepts": [ "Triangle Congruence Postulates", "HL Congruence Theorem" ] } ## Identify given geometric properties $$ \begin{aligned} &\overline{PS} \cong \overline{RQ} \quad \text{(Hypotenuses of right triangles)} \ &\angle PQS = 90^\circ, \quad \angle RSQ = 90^\circ \quad \text{(Right angles)} \end{aligned} $$ ## Identify shared side $$ \overline{QS} \cong \overline{SQ} \quad \text{(Reflexive Property of Congruence, shared leg)} $$ ## Apply right triangle congruence theorem $$ \begin{aligned} &\triangle SQR \text{ and } \triangle QSP \text{ are right triangles} \ &\text{Hypotenuses: } \overline{RQ} \cong \overline{PS} \ &\text{Legs: } \overline{QS} \cong \overline{SQ} \ &\therefore \triangle SQR \cong \triangle QSP \quad \text{by HL (Hypotenuse-Leg) Congruence Theorem} \end{aligned} $$

A. SSS Congruence Theorem

B. SAS Congruence Theorem

C. AAS Congruence Theorem

D. HL Congruence Theorem

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "HL Congruence Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given geometric properties

Identify shared side

Apply right triangle congruence theorem

Answer: