rectangle pqrs is shown with its diagonals, $\overline{pr}$ and $\overline{qs}$.

what type of triangle is $\delta str$?

- right triangle
- equilateral triangle
- isosceles triangle
- scalene triangle

Question

rectangle pqrs is shown with its diagonals, $\overline{pr}$ and $\overline{qs}$.

what type of triangle is $\delta str$?

- right triangle
- equilateral triangle
- isosceles triangle
- scalene triangle

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": [ "Properties of Rectangles" ], "new_concepts": [ "Triangle Classification" ], "current_concepts": [ "Properties of Rectangles", "Triangle Classification" ] } ## Identify properties of rectangle diagonals Using the *Properties of Rectangles* knowledge point $$ \begin{aligned} &PR = QS \quad \text{(Diagonals are equal in length)}\ &PT = TR = \frac{1}{2}PR \quad \text{(Diagonals bisect each other)}\ &ST = TQ = \frac{1}{2}QS \quad \text{(Diagonals bisect each other)} \end{aligned} $$ ## Determine relationship between segment lengths Using the *Properties of Rectangles* knowledge point $$ \begin{aligned} &TR = \frac{1}{2}PR\ &ST = \frac{1}{2}QS\ &PR = QS \implies ST = TR \end{aligned} $$ ## Classify the triangle Using the *Properties of Rectangles* knowledge point $$ \begin{aligned} &ST = TR \implies \triangle STR \text{ has two equal sides}\ &\text{Therefore, } \triangle STR \text{ is an isosceles triangle} \end{aligned} $$

right triangle

equilateral triangle

isosceles triangle

scalene triangle

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

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QUESTION IMAGE

Question

Explanation:

Identify properties of rectangle diagonals

Determine relationship between segment lengths

Classify the triangle

Answer: