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In the Pythagoras property, the triangle must be ___________ .
- a)obtuse-angled
- b)acute-angled
- c)right-angled
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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In the Pythagoras property, the triangle must be ___________ .a)obtuse...
The Pythagoras Property and Right-Angled Triangles
The Pythagoras property is a fundamental concept in geometry that relates to the lengths of the sides of a right-angled triangle. According to this property, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words, if we denote the lengths of the sides as a, b, and c (with c being the hypotenuse), then the Pythagoras property can be expressed as a^2 + b^2 = c^2.
The Options and their Meanings
To answer the question, let's examine the given options and their meanings:
a) Obtuse-angled: An obtuse-angled triangle is a triangle with one angle greater than 90 degrees.
b) Acute-angled: An acute-angled triangle is a triangle with all angles less than 90 degrees.
c) Right-angled: A right-angled triangle is a triangle with one angle exactly equal to 90 degrees.
d) None of these: This option implies that none of the above options are correct.
Explanation of the Correct Answer
The correct answer is option 'C' - right-angled. This is because the Pythagoras property specifically applies to right-angled triangles. The formula a^2 + b^2 = c^2 is only valid when dealing with right-angled triangles. The property allows us to find the length of one side of a right-angled triangle if we know the lengths of the other two sides.
Application of the Pythagoras Property
The Pythagoras property is widely used in various fields, including engineering, architecture, and physics. It is particularly useful when calculating distances, determining unknown side lengths, or verifying if a triangle is right-angled.
Conclusion
In conclusion, the Pythagoras property is a fundamental concept in geometry that applies specifically to right-angled triangles. The property states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This property has practical applications in various fields and is essential for solving problems involving right-angled triangles.
The Pythagoras property is a fundamental concept in geometry that relates to the lengths of the sides of a right-angled triangle. According to this property, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words, if we denote the lengths of the sides as a, b, and c (with c being the hypotenuse), then the Pythagoras property can be expressed as a^2 + b^2 = c^2.
The Options and their Meanings
To answer the question, let's examine the given options and their meanings:
a) Obtuse-angled: An obtuse-angled triangle is a triangle with one angle greater than 90 degrees.
b) Acute-angled: An acute-angled triangle is a triangle with all angles less than 90 degrees.
c) Right-angled: A right-angled triangle is a triangle with one angle exactly equal to 90 degrees.
d) None of these: This option implies that none of the above options are correct.
Explanation of the Correct Answer
The correct answer is option 'C' - right-angled. This is because the Pythagoras property specifically applies to right-angled triangles. The formula a^2 + b^2 = c^2 is only valid when dealing with right-angled triangles. The property allows us to find the length of one side of a right-angled triangle if we know the lengths of the other two sides.
Application of the Pythagoras Property
The Pythagoras property is widely used in various fields, including engineering, architecture, and physics. It is particularly useful when calculating distances, determining unknown side lengths, or verifying if a triangle is right-angled.
Conclusion
In conclusion, the Pythagoras property is a fundamental concept in geometry that applies specifically to right-angled triangles. The property states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This property has practical applications in various fields and is essential for solving problems involving right-angled triangles.
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In the Pythagoras property, the triangle must be ___________ .a)obtuse...
(c) right- angled
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In the Pythagoras property, the triangle must be ___________ .a)obtuse-angledb)acute-angledc)right-angledd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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