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 ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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, $A E = 3 c m$

Suggest Corrections

Similar questions

Q. 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

Q. 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

and

B P = 8 c m

, then DE is:

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

Q. In the given figure, D is the mid-point of AB and

P C = \frac{1}{2} A P = 3

cm. If

A D = D B = 4

cm and

D E | | B P

, then find the length of AE.

Join BYJU'S Learning Program

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, $A E = 3 c m$