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Which of the following is a justification used while probing the similarity of triangles MPN and triangle NPO?

Which of the following is a justification used while probing the similarity of triangles-example-1
User Pluke
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A justification used while probing the similarity of triangles MPN and NPO is the: C. definition of an altitude.

What is the definition of an altitude?

The altitude of a right triangle is a line segment drawn from the right-angle vertex perpendicular to the hypotenuse, forming two right-angled triangles.

In the given triangle MNO, where NP is an altitude from the right angle:

m∠PNO = 90° - m∠MNP.

m∠MPN = m∠NPO = 90° [Based on the definition of an altitude]

Using the angle sum property in triangle MNP, we have:

m∠MNP + m∠MPN + m∠PMN = 180°

Substitute:

m∠MNP + 90 + m∠PMN = 180°

m∠PMN = 90° - m∠MNP.

In triangles MNO and PNO,

m∠PMN = m∠PNO = 90° - m∠MNP, and

m∠MPN = m∠NPO = 90° (based on the definition of an altitude).

Thus, ΔMNO is similar to ΔPNO based on the AA similarity postulate.

We can therefore conclude that the justification we would use from the given options is: C. definition of an altitude.

User Raphel
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