right triangle abc is isosceles and point m is the midpoint of the hypotenuse.

what is true about triangle amb?

- it is congruent to triangle abc.
- it is an obtuse triangle.
- it is an isosceles right triangle.
- it is a scalene triangle.

Question

right triangle abc is isosceles and point m is the midpoint of the hypotenuse.

what is true about triangle amb?

- it is congruent to triangle abc.
- it is an obtuse triangle.
- it is an isosceles right triangle.
- it is a scalene triangle.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Isosceles Triangle Properties", "Triangle Angle Sum Theorem" ], "new_concepts": [ "Midpoint of Hypotenuse Theorem", "Right Triangle Geometry" ], "current_concepts": [ "Isosceles Triangle Properties", "Triangle Angle Sum Theorem", "Midpoint of Hypotenuse Theorem", "Right Triangle Geometry" ] } ## Determine the angles of right isosceles triangle ABC $$ \begin{aligned} &\angle B = 90^\circ\ &AB = BC \implies \angle A = \angle C = \frac{180^\circ - 90^\circ}{2} = 45^\circ \end{aligned} $$ ## Analyze the properties of segment BM $$ \begin{aligned} &AM = MC = \frac{AC}{2}\ &BM = \frac{AC}{2} \quad \text{(Median to hypotenuse theorem)}\ &AM = BM \implies \triangle AMB \text{ is isosceles} \end{aligned} $$ ## Calculate the angles of triangle AMB $$ \begin{aligned} &\angle BAM = \angle A = 45^\circ\ &\angle ABM = \angle BAM = 45^\circ \quad \text{(Base angles of isosceles } \triangle AMB\text{)}\ &\angle AMB = 180^\circ - (45^\circ + 45^\circ) = 90^\circ\ &\triangle AMB \text{ is an isosceles right triangle} \end{aligned} $$

It is congruent to triangle ABC.

It is an obtuse triangle.

It is an isosceles right triangle.

It is a scalene triangle.

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QUESTION IMAGE

Question

Explanation:

Determine the angles of right isosceles triangle ABC

Analyze the properties of segment BM

Calculate the angles of triangle AMB

Answer: