given that efgh is a parallelogram and $\angle hef$ is a right angle, which of the following statements about angles will prove that $\angle fgh$ is also a right angle?

* corresponding angles are congruent when parallel lines are cut by a transversal.
* opposite angles in a parallelogram are congruent.
* vertical angles are congruent.
* the base angles of an isosceles triangle are congruent.

Question

given that efgh is a parallelogram and $\angle hef$ is a right angle, which of the following statements about angles will prove that $\angle fgh$ is also a right angle?

* corresponding angles are congruent when parallel lines are cut by a transversal.
* opposite angles in a parallelogram are congruent.
* vertical angles are congruent.
* the base angles of an isosceles triangle are congruent.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parallelogram Properties" ], "new_concepts": [], "current_concepts": [ "Parallelogram Properties" ] } ## Identify the relationship between the given angles $$ \begin{aligned} &\text{Given: } EFGH \text{ is a parallelogram.} \ &\angle HEF \text{ and } \angle FGH \text{ are opposite angles in parallelogram } EFGH. \end{aligned} $$ ## Apply the relevant geometric property $$ \begin{aligned} &\text{Property: Opposite angles of a parallelogram are congruent.} \ &\angle FGH \cong \angle HEF \end{aligned} $$ ## Determine the measure of the target angle $$ \begin{aligned} &m\angle HEF = 90^\circ \implies m\angle FGH = 90^\circ \end{aligned} $$

Corresponding angles are congruent when parallel lines are cut by a transversal.

Opposite angles in a parallelogram are congruent.

Vertical angles are congruent.

The base angles of an isosceles triangle are congruent.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallelogram Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between the given angles

Apply the relevant geometric property

Determine the measure of the target angle

Answer: