Questions and Answers
The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
5.7 cm
The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tenth, what is the greatest possible value of x?
6.3
The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
8.5 cm
The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?
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The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possible whole-number value of x?
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Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches. What is the greatest possible whole-number length of the unknown side?
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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle?
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An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?
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Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
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Which set of numbers can represent the side lengths, in inches, of an acute triangle?
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Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
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Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
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Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm, is a right triangle?
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The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.
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Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet. Which is true regarding the triangular frame?
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Study Notes
Triangle Classification Theorems
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In an acute isosceles triangle, with the longest side measuring 8 cm, the minimum length of one of the congruent sides is approximately 5.7 cm.
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For an obtuse triangle with the longest side of 20 cm and shorter sides labeled as x cm and 3x cm, the maximum value of x rounds to 6.3 cm.
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In another acute isosceles triangle where the longest side is 12 cm, the minimum length for one congruent side is about 8.5 cm.
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Given an acute triangle with a longest side of 30 inches, the minimum possible perimeter, when both remaining sides are congruent, is approximately 72.44 inches.
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An acute triangle with shorter sides of x cm and 2x cm, with the longest side at 15 cm, has a smallest whole-number value for x equal to 7.
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In an obtuse triangle with sides measuring 12 inches, 14 inches, and an unknown third side equal to 14 inches, the largest possible integer length for the unknown side is 7 inches.
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For an acute triangle with two known sides measuring 10 cm and 16 cm, the third side must fall within the range of 12.5 cm to 18.9 cm.
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An acute triangle with sides measuring 8 cm and 10 cm has a possible third side range of greater than 6 cm and less than 12.8 cm.
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A right triangle can have side lengths of 10 cm, 24 cm, and 26 cm, satisfying the Pythagorean theorem.
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For an acute triangle, a valid set of side lengths is 5 inches, 7 inches, and 8 inches, all adhering to triangle inequality rules.
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A triangle with sides of 6 cm, 10 cm, and 12 cm is classified as obtuse since 6^2 + 10^2 is less than 12^2.
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A triangle with sides of 2 in., 5 in., and 4 in. is not acute because the condition 2^2 + 4^2 is less than 5^2 holds true.
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A triangle with side lengths of 5 cm, 13 cm, and 12 cm is a right triangle, fulfilling the equation 5^2 + 12^2 = 13^2.
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In a right triangle with lengths of 5 inches and 8 inches, the difference between possible lengths of the third side is 3.2 inches.
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In a scenario involving a right angle, with a vertical board height of 12 feet and a horizontal board 15 feet long, a supporting beam measuring 20 feet creates an obtuse triangle. Approximately 0.8 feet needs to be cut from the beam to form a right triangle.
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Test your knowledge of triangle classification theorems with these flashcards. Each card presents a unique problem related to isosceles and obtuse triangles, challenging you to apply the theorems correctly. Perfect for students preparing for exams in geometry.
