Triangle Inequality Theorem
A triangular garden has side lengths of 4 ft, 5 ft, and 10 ft. Does it form a triangle?
Answer: What is "No, because 4 + 5 = 9, which is not greater than 10"?
Two angles of a triangle are 40° and 60°, and the side length is 10 ft. Is this triangle unique?
Answer: What is "Many triangles, because the AAA rule only determines shape, not size"?
$100: A triangle has angles of 50° and 60°. What is the measure of the third angle?
Answer: What is "70°, because the angles must add to 180°"?
$100: A triangle has three equal sides of 10 m each. What type of triangle is it?
Answer: What is "An equilateral triangle"?
$100: A triangle has two sides of 6 ft and 8 ft. What is the range for the third side?
Answer: What is "2 ft < third side < 14 ft"?
$100: What is the sum of the angles in any triangle?
180
A builder plans to use pieces of wood measuring 6 in, 8 in, and 13 in for a frame. Does it form a triangle?
Answer: What is "yes, because 6 + 8 = 14, but the third side cannot equal the sum of the two shorter sides"?
A triangle has side lengths of 9 m, 9 m, and an included angle of 50°. How many triangles can be formed?
Answer: What is "One unique triangle"?
$200: A triangular flag has two angles of 80° each. What is the third angle?
Answer: What is "20°, because 80 + 80 + 20 = 180°"?
$200: A triangle has two equal sides and one base of 8 cm. What type of triangle is it?
Answer: What is "An isosceles triangle"?
$200: A triangular banner has sides of 7 in and 10 in. What is the smallest and largest possible length for the third side?
Answer: What is "3 in < third side < 17 in"?
$200: A triangle has sides of 3 m, 4 m, and 5 m. What type of triangle is it?
Answer: What is "A right triangle"?
A pool cover has sides of 7 m, 10 m, and 12 m. Does it form a triangle?
Answer: What is "Yes, because the sum of any two sides is greater than the third side"
A triangle has angles of 50°, 60°, and 70°. How many triangles can you make with these angles?
Answer: What is "Many triangles, since only the shape is determined by the angles"?
$300: One angle in a triangle is 90°. The second angle is 30°. What is the third angle?
Answer: What is "60°, because the total is 180°"?
$300: A construction worker creates a triangular window frame with sides of 5 m, 12 m, and 13 m. What type of triangle is it?
Answer: What is "A right triangle, scalene and unique triangle because 5² + 12² = 13²"?
$300: A tent forms a triangular shape with sides of 4 m and 9 m. What is the maximum possible length for the third side?
Answer: What is "Less than 13 m"?
$300: A triangular plot has angles of 50°, 60°, and 70°. How many triangles can you make with these angles?
Answer: What is "Many triangles, because angles do not determine size"?
A triangular playground has side lengths of 15 ft, 25 ft, and 35 ft. Does it form a triangle?
Answer: What is "yes, because 15 + 25 = 40, which is not greater than 35"?
Can you form a triangle with angles of 90°, 45°, and 45°?
What is "Yes, it is will make many triangle
$400: A triangle has angles of 35° and 45°. What type of triangle is it, and what is the third angle?
Answer: What is "An acute triangle with a third angle of 100°"?
$400: A triangular plot of land has sides of 9 m, 12 m, and 15 m. What type of triangle is it?
Answer: What is "A scalene triangle, because all sides are different"?
$400: A triangular signboard has two sides of 15 cm and 20 cm. What is the range for the third side?
Answer: What is "5 cm < third side < 35 cm"?
$400: If a triangle has angles of 80° and 55°, what is the third angle?
Answer: What is "45°"?
A shipping crate is in the shape of a triangle with sides measuring 8 cm, 11 cm, and 15 cm. Does it form a triangle?
Answer: What is "Yes, because all three conditions of the Triangle Inequality Theorem are met"?
A triangular roof has side lengths of 10 ft, 15 ft, and 25 ft. Is it a unique triangle?
Answer: What is "No triangle, because 10 + 15 = 25, and the sum of two sides cannot equal the third side"?
$500: A triangular yield sign has three equal angles. What is the measure of each angle?
Answer: What is "60°, because all angles in an equilateral triangle are equal and add to 180°"?
$500: A ramp is built in the shape of a triangle with a right angle. The two legs are equal in length. What type of triangle is it?
Answer: What is "An isosceles right triangle"?
$500: A triangular bridge has sides of 12 ft and 18 ft. What is the smallest possible length for the third side?
Answer: What is "6 ft"?
$500: A triangular signboard has sides of 6 ft, 6 ft, and 8 ft. What type of triangle is it?
Answer: What is "An isosceles triangle"?