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If ∠BAE = 45° and ∠CED = 70° is ΔABE ~ ΔCDE? If so, by what criterion?

Ayes, by AA criterion
Byes, by SAS criterion
Cyes, by SSA criterion
Dno, not possible to tell.

If BAE = 45 and CED = 70 is ΔABE ΔCDE? If so, by what criterion? A) yes, by AA criterion B) yes, by SAS criterion C) yes, by SSA criterion D) no, not possible t class=

Verified Answer :

Answer:

ΔABE ~ ΔCDE by AA criterion .

Option (A) is correct .

Step-by-step explanation:

As given

∠BAE = 45° and ∠CED = 70°

Now in the ΔABE .

By apply angle sum property of a triangles .

∠ABE + ∠BEA + ∠BAE = 180 °

(As ∠BAE = 45° , ∠ABE = 65°)

65 + ∠BEA + 45 = 180 °

∠BEA = 180° - (65+45)°

∠BEA = 180° - 110°

∠BEA = 70°

As in ΔCED .

∠CDE + ∠DEC + ∠ECD = 180°

(As  ∠CED = 70° , ∠CDE = 65°)

65 + 70+ ∠ECD = 180°

∠ECD = 180° - (65+70)°

∠ECD = 180° - 135°

∠ECD = 45°

Now in the ΔABE and ΔCDE .

(1)  ∠BAE =∠ECD = 45°

(2) ∠BEA=∠CED = 70°

(3) ∠ABE = ∠CDE = 65°

Thus  ΔABE ~ ΔCDE by AA criterion .

Option (A) is correct .



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