In the given figure- AC - CE and AB - ED- The value of x is - nbsp-units- 15202530

The correct option is A 15In Δ ABC and Δ EDC, AC = CE nbsp; (given) Also, AB∥DE and AE is a transversal. ⇒∠ BAC= ∠ DEC nbsp; nbsp; [alternate interior ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

ASA Rule

In the given ...

Question

In the given figure, AC = CE and AB $∥$ ED. The value of $x$ is ___ units.

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

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

Open in App

Solution

The correct option is A 15
$In Δ A B C and Δ E D C$ ,
AC = CE (given)
Also, AB $∥$ DE and AE is a transversal.
$\Rightarrow ∠ B A C = ∠ D E C$ [alternate interior angles]
$∠ A C B = ∠ E C D$ [vertically opposite angles]
$∴ Δ A B C ≅ Δ E D C$ (ASA congruence criterion)
$\Rightarrow A B = D E$ (CPCT)
$\Rightarrow x + 10 = 2 x - 5$
$\Rightarrow x = 15$ units

Suggest Corrections

Similar questions

Q. In the given figure, AC = CE and AB

∥

ED. The value of

x

is ___ units.

In the given figure, AC = CE and AB $∥$ ED. The value of x is ___ units.

Q. In the given figure, AC = CE and AB || ED. Then the value of x = ________ units.

If in the given figure, AC = CE and AB

∥

ED, then the value of

x

is 15 units.

Q. (a) In the given figure, show that

Δ A M P ≅ Δ A M Q

(b)

In the given figure, AC = CE and AB

∥

ED. The value of

x

is ___ units.
[4 MARKS]

Join BYJU'S Learning Program

In the given figure, AC = CE and AB ∥ ED. The value of x is ___ units.

The correct option is A 15In ΔABC and ΔEDC, AC = CE (given) Also, AB∥DE and AE is a transversal. ⇒∠BAC=∠DEC [alternate interior angles] ∠ACB=∠ECD [vertically opposite angles] ∴ΔABC≅ΔEDC (ASA congruence criterion) ⇒AB=DE (CPCT) ⇒x+10=2x−5 ⇒x=15 units

In the given figure, AC = CE and AB $∥$ ED. The value of $x$ is ___ units.