For a triangle ABC- which of the following is-are true-A- A B2-B C2-A C2B- AB - BC - ACC- AB - AC - BC-D- AB - BC - AC

The correct options are B AB + BC gt; AC C AB AC lt; BC. AB^2 + BC^2 = AC^2 will be satisfied, if the the triangle is a right angled triangle. Sum of a ...

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Standard VII

Mathematics

Area of Squares

For a triangl...

Question

For a triangle ABC, which of the following is/are true?

A B^{2} + B C^{2} = A C^{2}

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A B + B C > A C

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A B - A C < B C

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A B + B C = A C

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Solution

The correct options are
B $A B + B C > A C$
C $A B - A C < B C$ .

$A B^{2} + B C^{2} = A C^{2}$
will be satisfied, if the the triangle is a right-angled triangle.

Sum of any two sides of the triangle is greater than the third side.
Hence, $A B + B C > A C$ is true.

The difference between any two sides of a triangle is lesser than the third side.
So, $A B - A C < B C$ .

Sum of any two sides of the triangle is greater than the third side. By this property, $A B + B C = A C$ will not be true.

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In a right angled $Δ A B C$ , if $∠ B = 90^{\circ}$ , then which of the following is true?

a) $A B^{2} = B C^{2} + A C^{2}$
b) $A C^{2} = A B^{2} + B C^{2}$
c) $A B = B C + A C$
d) $A C = A B + B C$

For a $△ A B C (A B - A C) > B C$

Q. In triangle ABC, right angled at B, Find the expressions of cos A , sin C, tan A and cot C.

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