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

A) ∠BDC and ∠AED are right angles
B) AE ≅ ED
C) △BDC is a right triangle
D) ∠DBC ≅ ∠DCB

Which piece of additional information can be used to prove CEA CDB A BDC and AED are right angles B AE ED C BDC is a right triangle D DBC DCB class=

Respuesta :

InesWalston

Answer-

The correct answer is

∠BDC and ∠AED are right angles

Solution-

In the ΔCEA and ΔCDB,

[tex]m\angle BCD=m\angle ACE[/tex]

As this common to both of the triangle.

If ∠BDC and ∠AED are right angles, then [tex]m\angle E=90=m\angle D[/tex]

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.


aksnkj

Two triangles △CEA and △CDB are similar. Option A "∠BDC and ∠AED are right angles" is sufficient to prove that the given triangles are similar.

It is required to prove △CEA  is similar to △CDB.

From the given figure, if we choose ∠BDC and ∠AED are right angles, then the following conclusions can be made:

  • ∠BDC and ∠AED are perpendicular on the same side EC.
  • AE and BD will be parallel because ∠BDC and ∠AED are equal.
  • Now, AC is the intersecting side, and AE and BD are parallel. SO, the angles CAE and CBD will also be equal because they are corresponding angles.

From the above conclusions, it can be said that △CEA  is similar to △CDB because they have two equal angles and AA similarity criteria are fulfilled.

Therefore, option A "∠BDC and ∠AED are right angles" is sufficient to prove that the given triangles are similar.

For more details, refer to the link:

https://brainly.com/question/20502277

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