Question

question 5
yara says, \with respect to its side lengths, another name for this polygon is a ___ triangle.\ select the answer that
correctly fills in the blank, and select the reason that it does.
\\( \square \\) equilateral
\\( \square \\) two angles of the triangle measure only \\( 1^{\circ} \\) apart from each other, so it is an isosceles triangle.
\\( \square \\) isosceles
\\( \square \\) since it was determined that it is a three - sided polygon, it must be an equilateral triangle.
\\( \square \\) scalene
\\( \square \\) since the three angle measures are different, all three side lengths must also be different.

Explanation:

• An equilateral triangle has all three sides equal and all three angles equal (each \(60^{\circ}\)). The given reason for equilateral is incorrect as just being a three - sided polygon doesn't make it equilateral.
• An isosceles triangle has at least two sides equal and at least two angles equal. The reason given for isosceles (two angles \(1^{\circ}\) apart) is not a valid definition of an isosceles triangle.
• A scalene triangle has all three sides of different lengths and all three angles of different measures. The property that if all three angle measures are different, then all three side lengths must also be different is a valid property of triangles (by the Law of Sines \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\), where \(a,b,c\) are side lengths and \(A,B,C\) are angle measures). If \(A

eq B
eq C\), then \(a
eq b
eq c\).

Answer:

scalene, Since the three angle measures are different, all three side lengths must also be different.