Question

Which piece of additional information can be used to prove △CEA ~ △CDB?

Answer 1

Answer-

The correct answer is

∠BDC and ∠AED are right angles

Solution-

In the ΔCEA and ΔCDB,

$m\angle BCD=m\angle ACE$

As this common to both of the triangle.

If ∠BDC and ∠AED are right angles, then $m\angle E=90=m\angle D$

Now as

∠BCD = ∠ACE and ∠BDC = ∠AED,

∠DBC and ∠EAC will be same. (as sum of 3 angles in a triangle is 180°)

Then, ΔCEA ≈ ΔCDB

Therefore, additional information can be used to prove ΔCEA ≈ ΔCDB is ∠BDC and ∠AED are right angles.

Answer 2

Answer:

Step-by-step explanation:

If we take that ∠BDC and ∠AED are right angles, then m∠AEC=m∠BDC=90°.

Then from ΔCEA and ΔCDB, we have

m∠BCD=m∠ACE( Common)

m∠AEC=m∠BDC( Each 90°)

with this, ∠DBC and ∠EAC will also be equal.

thus, ΔCEA is similar to ΔCDB.

And the additional information can be  ∠BDC and ∠AED are right angles.

Hence, option A is correct.

Only △BDC being a right triangle cannot fulfill the conditions, thus this option is incorrect.

Moreover,  AE ≅ ED and ∠DBC ≅ ∠DCB  does not help in making the two triangles similar.