question 11 of 25

based on the information marked in the diagram, $\delta pqr$ and $\delta stu$ must be congruent.

a. true
b. false

Question

question 11 of 25

based on the information marked in the diagram, $\delta pqr$ and $\delta stu$ must be congruent.

a. true
b. false

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence Postulates", "Right Triangle Congruence Theorems", "LA Congruence Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Congruence Postulates", "Right Triangle Congruence Theorems", "LA Congruence Theorem" ] } ## Identify the given markings Using the *Triangle Congruence Postulates* and *Right Triangle Congruence Theorems* knowledge points $$ \begin{aligned} &\angle P \cong \angle S \quad (\text{both are } 90^\circ \text{ right angles})\ &\overline{QR} \cong \overline{TU} \quad (\text{hypotenuses with single tick marks})\ &\angle R \cong \angle U \quad (\text{acute angles with single arcs}) \end{aligned} $$ ## Apply right triangle congruence Using the *LA Congruence Theorem* and *Right Triangle Congruence Theorems* knowledge points $$ \begin{aligned} &\text{In right triangles } \triangle PQR \text{ and } \triangle STU:\ &\text{Hypotenuse: } \overline{QR} \cong \overline{TU}\ &\text{Acute Angle: } \angle R \cong \angle U\ &\text{By HA (Hypotenuse-Angle) Congruence: } \triangle PQR \cong \triangle STU \end{aligned} $$ ## Evaluate the statement The statement claims that $\triangle PQR$ and $\triangle STU$ must be congruent. Since we have proven congruence using the HA theorem (which is a specific case of AAS), the statement is true.

A. True

B. False

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

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QUESTION IMAGE

Question

Explanation:

Identify the given markings

Apply right triangle congruence

Evaluate the statement

Answer: