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Construction of Right Angled Triangle: Given Length of One Leg and its Hypotenuse Video Lecture | Mathematics for Grade 7

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FAQs on Construction of Right Angled Triangle: Given Length of One Leg and its Hypotenuse Video Lecture - Mathematics for Grade 7

1. How can I construct a right-angled triangle if I know the length of one leg and its hypotenuse?
Ans. To construct a right-angled triangle when the length of one leg and its hypotenuse are given, you can follow these steps: 1. Draw a line segment representing the given length of the leg. 2. From one end of the line segment, draw a perpendicular line. 3. Measure the given length of the hypotenuse from the other end of the line segment. 4. Connect the endpoint of the perpendicular line to the endpoint of the hypotenuse using a straight line segment. 5. The resulting triangle is a right-angled triangle.
2. Can I construct a right-angled triangle if the length of one leg and its hypotenuse are the same?
Ans. No, it is not possible to construct a right-angled triangle if the length of one leg and its hypotenuse are the same. In a right-angled triangle, the hypotenuse is always longer than both legs. If the length of one leg and the hypotenuse are equal, it violates the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
3. What is the Pythagorean theorem?
Ans. The Pythagorean theorem is a fundamental principle in geometry. It 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. Mathematically, it can be represented as a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.
4. How can I verify if a triangle is right-angled using the lengths of its sides?
Ans. To verify if a triangle is right-angled using the lengths of its sides, you can use the Pythagorean theorem. Follow these steps: 1. Identify the longest side of the triangle, which is the hypotenuse. 2. Square the lengths of the other two sides. 3. Add the squared lengths of the other two sides. 4. If the sum of the squares of the shorter sides is equal to the square of the longest side, then the triangle is right-angled.
5. Can a right-angled triangle have two equal legs?
Ans. Yes, a right-angled triangle can have two equal legs. Such a triangle is called an isosceles right-angled triangle. In an isosceles right-angled triangle, the two shorter sides, which are the legs, are equal in length, and the longer side, which is the hypotenuse, is the square root of two times the length of the legs.
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