Pregunta
Which statement is true?
A scalene triangle and a right triangle are always congruent.
A scalene triangle and a right triangle are never congruent.
An equilateral triangle and a right triangle are always congruent.
An equilateral triangle and a right triangle are never congruent.
A scalene triangle and a right triangle are always congruent.
A scalene triangle and a right triangle are never congruent.
An equilateral triangle and a right triangle are always congruent.
An equilateral triangle and a right triangle are never congruent.
Ask by Wade Hobbs. in the United States
Jan 30,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
An equilateral triangle and a right triangle are never congruent.
Solución
The correct statement is:
An equilateral triangle and a right triangle are never congruent.
Explanation:
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Scalene Triangle and Right Triangle:
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Option 1: “A scalene triangle and a right triangle are always congruent.”
This is false. While some scalene triangles can be right triangles (e.g., a 3-4-5 triangle), not all scalene triangles are right-angled, and vice versa. Hence, they are not always congruent. -
Option 2: “A scalene triangle and a right triangle are never congruent.”
This is also false. As mentioned, there are cases where a scalene triangle can be a right triangle, making them congruent in those specific instances.
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Equilateral Triangle and Right Triangle:
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Option 3: “An equilateral triangle and a right triangle are always congruent.”
This is false. An equilateral triangle has all three angles equal to 60 degrees, whereas a right triangle has one 90-degree angle. Therefore, they cannot be congruent. -
Option 4: “An equilateral triangle and a right triangle are never congruent.”
This is true. Due to the difference in their internal angles and side properties, an equilateral triangle cannot be congruent to a right triangle under any circumstances.
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Final Answer:
An equilateral triangle and a right triangle are never congruent.
An equilateral triangle and a right triangle are never congruent.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
A scalene triangle is defined as a triangle with all sides of different lengths, while a right triangle is characterized by having one angle equal to 90 degrees. Since a scalene triangle can take on a variety of shapes, including possibilities that are right-angled, it means that these two types of triangles can occasionally be congruent, but it’s not guaranteed. So, the statement that a scalene triangle and a right triangle are never congruent is indeed true!
Moving on to equilateral triangles, they have all three sides of equal length and all angles equal to 60 degrees, while right triangles include at least one right angle. Because the properties of these two triangle types are fundamentally different, there’s no situation where an equilateral triangle can also satisfy the conditions of being a right triangle, making it true that an equilateral triangle and a right triangle are never congruent.
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