Triangles (Understanding Right-angled triangles, Isosceles triangles, Equilateral triangles, Isosceles right-angled triangles and Unequal triangles)：練習問題

Which of the following sets of side lengths can be used to form a triangle?

If a triangle is equilateral and the length of one side is \(12\text{ cm}\), what is the size of each of its interior angles?

Two sides of a triangle are \(6\text{ cm}\) and \(9\text{ cm}\) long. Which of the following cannot be the length of the third side?

In a right-angled triangle, what is the measure of the largest angle?

An isosceles triangle has two sides that are each \( 7\text{ cm} \) long. Which of the following cannot be the length of the third side?

A triangle has three sides of lengths \(6\text{ cm}\), \(8\text{ cm}\), and \(10\text{ cm}\). Since all three sides have different lengths, what is the specific mathematical name for this type of triangle?

A student has two straws of lengths \(6\text{ cm}\) and \(9\text{ cm}\). If they want to form a triangle using a third straw with a whole number length, what is the shortest possible length (in \(\text{cm}\)) the third straw can be?

In a right-angled triangle, one acute angle is \(30^\circ\) smaller than the other. What is the measure of the smallest angle, and is this triangle scalene or isosceles?

A boat travels in a triangular path. The first leg of the trip is \(12\text{ km}\), the second leg is \(12\text{ km}\), and the third leg is \(15\text{ km}\).
a) What type of triangle is formed by the boat's path based on the lengths of the legs?
b) If the boat changed its third leg to be \(12\text{ km}\) instead of \(15\text{ km}\), what would the new name of the triangle be?
c) Calculate the total distance the boat travels in the second scenario where all three legs are each \(12\text{ km}\).

On a map, three cities form a triangle. The distance between City A and City B is \(40\text{ km}\), and the distance between City B and City C is also \(40\text{ km}\). The angle at City B is a right angle.
a) What is the most specific name for the triangle formed by these three cities?
b) If the distance from City A to City C is approximately \(57\text{ km}\), what is the perimeter of the triangle formed by the three cities?
c) If a pilot flies from City A to City C but must stop at a point exactly halfway between them, how far is that point from City A?