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

A triangle has angles measuring \(90^\circ\), \(45^\circ\), and \(45^\circ\). What is the specific name for this triangle?

Triangle ABC has two sides that are both 10 cm long, and the angle between them is \(90^\circ\). What is the best name for this triangle?

Triangle PQR is an isosceles right-angled triangle. If the side opposite the right angle is the longest side, and the other two sides are both \(12\) cm, what is the area of this triangle?

Which of the following descriptions accurately defines an unequal triangle (scalene triangle)?

Triangle ABC has side lengths \( 8 \text{ cm} \), \( 15 \text{ cm} \), and \( 17 \text{ cm} \). One of its angles is \( 90^\circ \). What is the specific type of this triangle?

A triangle has side lengths of 9 cm, 12 cm, and 15 cm. Since all three sides have different lengths, what is the specific name for this triangle based on its sides?

An isosceles right-angled triangle has one angle of \( 90^\circ \). What is the size of each of its other two angles?

Can a triangle be formed with side lengths of \( 7 \) cm, \( 10 \) cm, and \( 18 \) cm? Explain your answer.

Consider the following descriptions of three different triangles:
Triangle P: All three sides are 15 cm long.
Triangle Q: Two sides are 10 cm long, and the angle between them is 90 degrees.
Triangle R: Two sides are 12 cm long, and the third side is 8 cm long.

Identify the specific names for Triangle P, Triangle Q, and Triangle R.

A student is given three sticks of lengths 8 cm, 8 cm, and 16 cm.

(a) Can these sticks be used to form a triangle? Explain using the property of triangle side lengths.
(b) If the student replaces the 16 cm stick with a 12 cm stick, what is the specific name of the triangle formed?
(c) If the student replaces the 16 cm stick with an 8 cm stick, what is the specific name of the triangle formed?