If in ∆ABC , ∠C = 90° , CD⏊AB, CD = h, BC = a, CA = b and AB = c, prove that 1/h² = 1/a² + 1/b².

Step-by-step explanation:

In ∆ ABC, ∠C = 90°, CD ⏊ AB, CD =h, BC = a, CA = b, AB = c, Prove that

Given that,

In ∆ABC, ∠C = 90° and BC = a, CA = b, AB = c

So, Area of ∆ ABC is given by

Also,

In ∆ ABC, CD ⏊ AB

So, Area of ∆ABC is given by

From equation (1) and (2), we get

Again, In right ∆ ABC

Using Pythagoras Theorem, we have

On substituting the value of c, from equation (3), we get

can be rewritten as

Hence, Proved.

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1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem:

If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

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step-by-step explanation:

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step-by-step explanation: