Radii ok and nl are perpendicular to om because of the radius-tangent theorem. by definition of perpendicular, angles kom and lnm are right angles. this means that triangles kom and lnm are right triangles. angle lmn is common to both right triangles, so by the triangles kom and lnm are similar.
Angle Angle Angle (AAA) property
A right angled triangle is a triangle that has one of its angles to equal . It could be in the form of an isosceles triangle or an acute angled triangle.
The given question compares the congruence properties of two triangles, KOM and LNM.
<KOM = <LNM (right angle theorem)
<LMN = <KMO (common angles to both triangles)
⇒ <OKM = <NLM (property of a triangle i.e sum of angle in a triangle is )
ΔKOM = ΔLNM (congruence property)
Therefore, by angle angle angle (AAA) congruence property, the two triangles are similar.
GivensAngles KOM and LNM are congruent, because both are right.Angle LNM is common to both triangles.
If two internal angles of two triangles are congruent, then the third angle is also congruent.
Therefore, the similarity is proven by AAA postulate, which states that if we have three corresponding angles congruent, then those triangles are similar.
Remember that similarity is about proportion between sides and congruence between angles.