Question

match the side and angle measures of each triangle to its correct classification.
right scalene
obtuse isosceles
obtuse scalene
acute equilateral
angle measures: (26^circ), (36^circ), (118^circ)
side lengths: (1.5) in., (2) in., (3) in.
angle measures: (22^circ), (68^circ), (90^circ)
side lengths: (5) in., (12) in., (13) in.
angle measures: (60^circ), (60^circ), (60^circ)
side lengths: (4) in., (4) in., (4) in.
angle measures: (38^circ), (38^circ), (104^circ)
side lengths: (6) in., (6) in., (11) in.

Explanation:

Step1: Analyze first triangle

Angle measures: \(26^\circ, 36^\circ, 118^\circ\) (one obtuse angle, \(118^\circ>90^\circ\)), side lengths: \(1.5\) in, \(2\) in, \(3\) in (all different, scalene). So classify as obtuse scalene.

Step2: Analyze second triangle

Angle measures: \(22^\circ, 68^\circ, 90^\circ\) (one right angle, \(90^\circ\)), side lengths: \(5\) in, \(12\) in, \(13\) in (all different, scalene). So classify as right scalene.

Step3: Analyze third triangle

Angle measures: \(60^\circ, 60^\circ, 60^\circ\) (all acute, and equal), side lengths: \(4\) in, \(4\) in, \(4\) in (all equal, equilateral). So classify as acute equilateral.

Step4: Analyze fourth triangle

Angle measures: \(38^\circ, 38^\circ, 104^\circ\) (one obtuse angle, \(104^\circ>90^\circ\), two equal angles), side lengths: \(6\) in, \(6\) in, \(11\) in (two equal sides, isosceles). So classify as obtuse isosceles.

Answer:

• Angle measures \(26^\circ, 36^\circ, 118^\circ\), side lengths \(1.5\) in, \(2\) in, \(3\) in → obtuse scalene
• Angle measures \(22^\circ, 68^\circ, 90^\circ\), side lengths \(5\) in, \(12\) in, \(13\) in → right scalene
• Angle measures \(60^\circ, 60^\circ, 60^\circ\), side lengths \(4\) in, \(4\) in, \(4\) in → acute equilateral
• Angle measures \(38^\circ, 38^\circ, 104^\circ\), side lengths \(6\) in, \(6\) in, \(11\) in → obtuse isosceles