In the given figure- D is the mid-point of AB and PC -1-2 AP -3 cm - If AD - DB -4 cm and DE BP- then AE -A- 4 cmB- 8 cmC- 3 cmD- 5 cm

The correct option is C 3 cmGiven∶ 1/2 AP=3 cm ∴ AP=6 cm D is the mid point and DE∥ BP ⇒ E is the mid point of AP [Converse of mid point theorem] ∴ AE=1/2 A ...

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Byju's Answer

Standard IX

Mathematics

Converse of Mid-Point Theorem

In the given ...

Question

In the given figure, $D$ is the mid-point of $A B$ and $P C = \frac{1}{2} A P = 3 c m .$ If $A D = D B = 4 c m$ and $D E ∥ B P$ , then $A E =$

4 cm

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8 cm

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3 cm

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5 cm

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Solution

The correct option is C 3 cm
Given∶ $\frac{1}{2} A P = 3 c m$
$∴ A P = 6 c m$
$D$ is the mid-point and $D E ∥ B P$
$\Rightarrow E$ is the mid-point of $A P$ [Converse of mid-point theorem]
$∴ A E = \frac{1}{2} A P = \frac{1}{2} \times 6 = 3 c m$
Hence, $A E = 3 c m$

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In the given figure, D is the mid-point of AB and PC=12AP=3 cm. If AD=DB=4 cm and DE∥BP, then AE=

The correct option is C 3 cmGiven∶ 12AP=3 cm ∴AP=6 cm D is the mid-point and DE∥BP ⇒E is the mid-point of AP [Converse of mid-point theorem] ∴AE=12AP=12×6=3 cm Hence, AE=3 cm

In the given figure, $D$ is the mid-point of $A B$ and $P C = \frac{1}{2} A P = 3 c m .$ If $A D = D B = 4 c m$ and $D E ∥ B P$ , then $A E =$

The correct option is C 3 cm
Given∶ $\frac{1}{2} A P = 3 c m$
$∴ A P = 6 c m$
$D$ is the mid-point and $D E ∥ B P$
$\Rightarrow E$ is the mid-point of $A P$ [Converse of mid-point theorem]
$∴ A E = \frac{1}{2} A P = \frac{1}{2} \times 6 = 3 c m$
Hence, $A E = 3 c m$