This triangle satisfies the Pythagorean theorem (5² + 12² = 13²), thus it is a right triangle.

Area = 1/2 * base * height. Therefore, 24 = 1/2 * 8 * height, which gives height = 6 cm.

The area of a triangle is given by the formula Area = 1/2 * base * height. Thus, 24 = 1/2 * 8 * height, which gives height = 6 cm.

Substituting the values into the area formula: A = 1/2 * 10 * 5 = 25 cm².

A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, thus it is a right triangle.

In an equilateral triangle, all sides are equal. Therefore, if the perimeter is 36 cm, each side is 36/3 = 12 cm.

Let the length of each equal side be x. The perimeter is given by 2x + 8 = 24. Solving for x gives 2x = 16, so x = 8 cm.

The perimeter is the sum of all sides. Therefore, base = 24 - (10 + 10) = 4 cm.

A triangle with sides in the ratio 3:4:5 is a right-angled triangle, as it satisfies the Pythagorean theorem.

A triangle with two equal angles is an isosceles triangle.

According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides and greater than the difference of the two sides. Therefore, the range is 3 cm to 17 cm.

According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.

Using the property that the sum of angles in a triangle is 180 degrees, angle C can be calculated as 180 - (30 + 60) = 90 degrees.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

Since two angles are equal (45 degrees each), triangle DEF is an isosceles triangle.

Using the Pythagorean theorem, hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Using the Pythagorean theorem, since 10^2 = 8^2 + 6^2 (100 = 64 + 36), triangle XYZ is a right triangle.

To find the length of side XZ when two sides and the included angle are known, the Cosine rule is applicable.

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

Using the Pythagorean theorem, since 5^2 + 12^2 = 25 + 144 = 169 = 13^2, triangle XYZ is a right triangle.

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

The longest side in triangle XYZ is XZ, which measures 10 cm.

The area of a triangle is given by the formula (1/2) * base * height. Thus, Area = (1/2) * 10 * 5 = 25 cm².

The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. Only 6, 8, and 10 satisfy this condition.

An isosceles triangle is defined as having at least two sides that are equal in length.

Similar triangles have equal corresponding angles, but their sides are in proportion, not necessarily equal.

An isosceles triangle has two equal sides and the angles opposite those sides are equal, but it does not have all angles equal unless it is also equilateral.

Not all triangles have all angles acute; for example, a right triangle has one angle that is 90 degrees.

A quadrilateral is a four-sided figure and not a type of triangle.

In an equilateral triangle, all sides are equal and all angles measure 60 degrees.