Question

determine if each triangle is scalene, isosceles, or equilateral.

Explanation:

Step1: Recall triangle type definitions

• Scalene triangle: All sides are of different lengths.
• Isosceles triangle: At least two sides are of equal length.
• Equilateral triangle: All three sides are of equal length.

Step2: Analyze each triangle

• First triangle (right - angled with two equal - marked sides):

Since two sides are marked as equal (by the tick marks), it is an isosceles triangle.

• Second triangle (all sides \(54\) in):

All three sides are \(54\) inches. So, by the definition of an equilateral triangle (all sides equal), it is an equilateral triangle.

• Third triangle (two equal - marked sides):

Two sides are marked as equal (by the tick marks). So, it is an isosceles triangle.

• Fourth triangle (sides \(7\) ft, \(4\) ft, \(10\) ft):

\(7
eq4
eq10\). All sides are of different lengths. So, it is a scalene triangle.

• Fifth triangle (sides \(27\) in, \(21\) in, \(30\) in):

\(27
eq21
eq30\). All sides are of different lengths. So, it is a scalene triangle.

• Sixth triangle (three equal - marked sides):

All three sides are marked as equal (by the tick marks). So, it is an equilateral triangle.

• Seventh triangle (angles \(29^{\circ},113^{\circ},38^{\circ}\)):

Since all angles are different, the sides opposite to these angles (by the law of sines \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)) will be different. So, it is a scalene triangle.

• Eighth triangle (sides \(31\) yd, \(26\) yd, \(38\) yd):

\(31
eq26
eq38\). All sides are of different lengths. So, it is a scalene triangle.

• Ninth triangle (two equal - marked sides):

Two sides are marked as equal (by the tick marks). So, it is an isosceles triangle.

Answer:

Isosceles, Equilateral, Isosceles, Scalene, Scalene, Equilateral, Scalene, Scalene, Isosceles