Question

Step 2: 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.

Answer 1

Angle Angle Angle (AAA) property

Explanation:

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Answer 2

Angle Angle Angle (AAA) property

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.