question 10 of 25

which of the following are congruence theorems for right triangles?

check all that apply.

a. ll
b. hh
c. ha
d. aa
e. la
f. hl

Question

question 10 of 25

which of the following are congruence theorems for right triangles?

check all that apply.

a. ll
b. hh
c. ha
d. aa
e. la
f. hl

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "HL Congruence Theorem" ], "new_concepts": [ "Right Triangle Congruence Theorems", "LL Congruence Theorem", "LA Congruence Theorem" ], "current_concepts": [ "HL Congruence Theorem", "Right Triangle Congruence Theorems", "LL Congruence Theorem", "LA Congruence Theorem", "HA Congruence Theorem" ] } ## Identify right triangle congruence criteria Using the **HL Congruence Theorem** knowledge point $$ \text{Right triangles have a fixed } 90^\circ \text{ angle, reducing required congruence parts to two.} $$ ## Evaluate LL and HH options Using the **HL Congruence Theorem** knowledge point $$ \begin{aligned} &\text{LL (Leg-Leg): Equivalent to SAS (congruent).} \ &\text{HH (Hypotenuse-Hypotenuse): Only one side pair, insufficient.} \end{aligned} $$ ## Evaluate HA and AA options Using the **HL Congruence Theorem** knowledge point $$ \begin{aligned} &\text{HA (Hypotenuse-Angle): Equivalent to AAS (congruent).} \ &\text{AA (Angle-Angle): Only shows similarity, insufficient.} \end{aligned} $$ ## Evaluate LA and HL options Using the **HL Congruence Theorem** knowledge point $$ \begin{aligned} &\text{LA (Leg-Angle): Equivalent to ASA or AAS (congruent).} \ &\text{HL (Hypotenuse-Leg): Equivalent to SSA for right triangles (congruent).} \end{aligned} $$

A. LL

B. HH

C. HA

D. AA

E. LA

F. HL

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

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QUESTION IMAGE

Question

Explanation:

Identify right triangle congruence criteria

Evaluate LL and HH options

Evaluate HA and AA options

Evaluate LA and HL options

Answer: