Step 2: Radii OK and NL are perpendicular to OM because of the radius-tangent theorem. By definition of perpendicular, angles KO

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Step 2: Radii OK and NL are perpendicular to OM because of the radius-tangent theorem. By definition of perpendicular, angles KO

M 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.

Mathematics

1 answer:

solong [7] · Answer 1 · 2020-08-28T13:16:13+03:00

Answer:

Angle Angle Angle (AAA) property

Step-by-step explanation:

A right angled triangle is a triangle that has one of its angles to equal $90^{0}$ . 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.

Thus,

<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 $180^{0}$ )

ΔKOM = ΔLNM (congruence property)

Therefore, by angle angle angle (AAA) congruence property, the two triangles are similar.