$\overleftrightarrow{rt}$ is a perpendicular bisector of $\overline{uv}$.

what is true of any triangle created by points u, v, and any point on $\overleftrightarrow{rt}$ other than s?

- it will be a right triangle.
- it will be an acute triangle.
- it will be an equilateral triangle.
- it will be an isosceles triangle.

Question

$\overleftrightarrow{rt}$ is a perpendicular bisector of $\overline{uv}$.

what is true of any triangle created by points u, v, and any point on $\overleftrightarrow{rt}$ other than s?

- it will be a right triangle.
- it will be an acute triangle.
- it will be an equilateral triangle.
- it will be an isosceles triangle.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Perpendicular Bisector Theorem" ], "current_concepts": [ "Perpendicular Bisector Theorem", "Isosceles Triangles" ] } ## Apply the Perpendicular Bisector Theorem $$ \begin{aligned} &\text{Let } P \text{ be any point on line } \overleftrightarrow{RT} \text{ other than } S.\ &\text{Since } \overleftrightarrow{RT} \text{ is the perpendicular bisector of segment } \overline{UV},\ &PU = PV. \end{aligned} $$ ## Classify the resulting triangle $$ \begin{aligned} &\text{Consider } \triangle UVP \text{ formed by points } U, V, \text{ and } P.\ &\text{Since } PU = PV \text{ and } P eq S \text{ (so } P, U, V \text{ are non-collinear),}\ &\triangle UVP \text{ must be an isosceles triangle.} \end{aligned} $$

It will be a right triangle.

It will be an acute triangle.

It will be an equilateral triangle.

It will be an isosceles triangle.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Bisector Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the Perpendicular Bisector Theorem

Classify the resulting triangle

Answer: