Answer:
The correct answer is option B. AA
Step-by-step explanation:
Given two triangle:
[tex]\triangle ABC[/tex] and [tex]\triangle WXY[/tex].
The dimensions given in [tex]\triangle ABC[/tex] are:
[tex]\angle A = 27^\circ\\\angle B = 90^\circ[/tex]
We know that the sum of three angles in a triangle is equal to [tex]180^\circ[/tex].
[tex]\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 27+90+\angle C=180^\circ\\\Rightarrow \angle C = 63^\circ[/tex]
The dimensions given in [tex]\triangle WXY[/tex] are:
[tex]\angle Y = 63^\circ\\\angle X = 90^\circ[/tex]
We know that the sum of three angles in a triangle is equal to [tex]180^\circ[/tex].
[tex]\angle W+\angle X+\angle Y = 180^\circ\\\Rightarrow \angle W+90+63=180^\circ\\\Rightarrow \angle W = 27^\circ[/tex]
Now, if we compare the angles of the two triangles:
[tex]\angle A = \angle W = 27^\circ\\\angle B = \angle X= 90^\circ\\\angle C = \angle Y= 63^\circ[/tex]
So, by AA postulate (i.e. Angle - Angle) postulate, the two triangles are similar.
[tex]\triangle ABC \sim \triangle WXY[/tex] by AA theorem.
So, correct answer is option B. AA
