Question

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 to tell.

Answer 1

ΔABE ~ ΔCDE by AA criterion .

Option (A) is correct .

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 .