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Assertion (A): Using the information in the given figure, we have PQ = 10 cm.

Using the information in the given figure, we have PQ = 10 cm. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

Reason (R): In right-triangle DAB, DB = 20 cm.

Using the information in the given figure, we have PQ = 10 cm. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

PQ=12BD=12×20cm=10cm\text{PQ} =\dfrac{1}{2}\text{BD}=\dfrac{1}{2}\times 20 \text{cm}= 10 \text{cm}

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Mid-point Theorem

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Answer

Both A and R are true.

Explanation

Given,

Using the information in the given figure, we have PQ = 10 cm. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

AB = 16 cm, AD = 12 cm

Using Pythagoras Theorem,

BD2 = AD2 + AB2

⇒ BD2 = 122 + 162

⇒ BD2 = 144 + 256

⇒ BD2 = 400

⇒ BD = 400\sqrt{400}

⇒ BD = 20 cm

Given, P is the mid point of DC.

Assuming Q as the mid point of BC,

In Δ BDC,

By mid-point theorem,

PQ // BD and

PQ = 12\dfrac{1}{2} BD

∴ PQ = 12×\dfrac{1}{2} \times 20 = 10 cm

Hence, both Assertion (A) and Reason (R) are true.

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