Question

If line QN bisects angle PQR and N is the midpoint of line PR classify each triangle by its angles and sides

Answer 1

Answer:

The answer is "Equiangular, Equilateral"

Step-by-step explanation:

please find the complete question in the file.

In this question, the answer is equiangular, in which the triangle was considered an equilateral triangle with 3 parallel inner angles. It's the measurement of each of these interior angles is 60 degrees, inside an equiangular triangle, and although there 3 parallel sides of an equiangular triangle, so it is just like an equilateral triangle.

Answer 2

Based on the sides and angles of a triangle, triangle PQR would be classified as: an equilateral triangle.

Recall:

• An equilateral triangle all three sides that are congruent and also has all of its three interior angles equal to 60 degrees each.

In the diagram given (see image attached below), we have the following:

PQ = RQ = 14 (congruent sides)

PN = NR = 7 (N is the midpoint of PR)

Therefore:

PR = PN + NR

• Substitute

PR = 7 + 7 = 14

This shows that triangle PQR has equal side lengths measuring 14 units (PQ = RQ = PR = 14).

• Also, we are given that:

m<QPR = m<QRP = 60 degrees (two congruent angles).

• Taking right triangle QNR into consideration,

m<NQR = 180 - (90 + 60) (sum of triangle)

m<NQR = 30 degrees

Therefore:

m<PQR = m<NQR + m<PQN

• Substitute

m<PQR = 30 + 30

m<PQR = 60 degrees.

This means that, triangle PQR has three equal angles measuring 60 degrees each (<PQR = <QPR = <QRP = 60 degrees).

Therefore, based on the sides and angles of a triangle, triangle PQR would be classified as: an equilateral triangle.

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