In triangleABC, AD is perpendicular toBC then show
that AB²- AC² = BD²-CD
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1
Answer:
Step-by-step explanation:
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Answered by
1
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
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