In the given figure- D is the mid-point of ABand PC-1-2 AP-3 cm- If AD-DB-4 cm and DE-BP - then AE is 3 cm5 cm8 cm4 cm

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

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Byju's Answer

Standard IX

Mathematics

Converse of Midpoint Theorem

In the given ...

Question

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

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 mid-point and $D E | | B P$
$\Rightarrow$ E is the mid-point of AP (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 ABand PC=12AP=3 cm. If AD=DB=4 cm and DE||BP , then AE is

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

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

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