what additional information do you need to know in order to prove the two triangles congruent using hl?

$\angle xyw \cong \angle wyz$
$\angle xwy \cong \angle zwy$
$xw \cong yz$
no additional information needed

Question

what additional information do you need to know in order to prove the two triangles congruent using hl?

$\angle xyw \cong \angle wyz$
$\angle xwy \cong \angle zwy$
$xw \cong yz$
no additional information needed

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": [ "HL Congruence Theorem" ], "new_concepts": [], "current_concepts": [ "HL Congruence Theorem", "Triangle Congruence Postulates" ] } ## Identify given geometric properties Using the *HL Congruence Theorem* knowledge point $$ \begin{aligned} &\angle X = 90^\circ, \quad \angle Z = 90^\circ \implies \triangle XYW \text{ and } \triangle ZWY \text{ are right triangles}\ &XY = WZ \quad (\text{marked legs})\ &WY = YW \quad (\text{shared hypotenuse by Reflexive Property}) \end{aligned} $$ ## Determine sufficiency for HL Congruence Using the *HL Congruence Theorem* knowledge point $$ \begin{aligned} &\text{Hypotenuse: } WY \cong YW\ &\text{Leg: } XY \cong ZW\ &\text{Right Angles: } \angle X \cong \angle Z\ &\implies \triangle XYW \cong \triangle ZWY \text{ by HL Theorem} \end{aligned} $$ ## Evaluate multiple-choice options Using the *HL Congruence Theorem* knowledge point $$ \begin{aligned} &\text{Since the triangles are already congruent by HL with given markings,}\ &\text{no additional information is needed.} \end{aligned} $$

$\angle XYW \cong \angle WYZ$

$\angle XWY \cong \angle ZWY$

$XW \cong YZ$

No additional information needed

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

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Question

Explanation:

Identify given geometric properties

Determine sufficiency for HL Congruence

Evaluate multiple-choice options

Answer: