Question

In triangleABC, AD is perpendicular toBC then show
that AB²- AC² = BD²-CD​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Since AD is perpendicular to BC, we get two right-angled triangles ABD and ADC

In triangle ABD, we have:

AB^2 = AD^2 + BD^2  (Using pythagoras theorem)        ...Eqn1

Similarly, in triangle ADC

AC^2 = AD^2 + CD^2  ......Eqn2

We can equate AD^2 from Eqn1 and Eqn2, and get:

AB^2 - BD^2 = AC^2 - CD^2

AB^2 - AC^2 = BD^2 - CD^2

Please see attached figure