Question

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Answer 1

Proved!

Step-by-step explanation:

In the given figure we can observe that, ΔADB and ΔADC are right angled triangle in which ∠D = 90° [AD ⊥ BC].

Pythagoras Theorem states that, in a right angled triangle, the square of hypotenuse is equal to the sum of square of other two sides.

In ΔADB,

• AB = Hypotenuse

In ΔADC,

• AC = Hypotenuse

Now let's apply Pythagoras theorem in both triangles:

Case 1: In ΔADB,

→ AB² = AD² + BD² ---[Eq.(i)]

Case 2: In ΔADC,

→ AC² = AD² + CD²

→ AD² = AC² - CD²

Substitute the value of AD² in [Eq.(i)],

→ AB² = AD² + BD²

→ AB² = AC² - CD² + BD²

→ AB² + CD² = AC² + BD²

Hence, proved!

Answer 2

Answer:

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