Question

Describe the angles and sides of an acute isosceles triangle.

Answer 1

Hint:
An isosceles triangle has any two of its sides equal.

Complete step by step solution:
An isosceles triangle is one that has any two of its sides equal, i.e. the length of any two sides are equal.
Now angles opposite to equal sides are equal. Therefore, an isosceles triangle must have two equal angles as it has two equal sides.
It is mentioned that the triangle is an acute-angled isosceles triangle. An acute angle is an angle greater than \[{0^ \circ }\] and less than \[{90^ \circ }\]. Therefore all the angles of this triangle are less than \[{90^ \circ }\].
Thus any acute angle isosceles triangle must have two equal sides 2 equal angles and all the angles must be less than \[{90^ \circ }\].

In the following diagram, an acute-angled isosceles triangle is shown:-

In the above diagram sides of, AB and AC are equal in length, hence their opposite angles are equal, that is $\angle ABC = \angle ACB$.

Note:
Note that angles can be classified as follows:
Acute angles are angles that are less than \[{90^ \circ }\].
Obtuse angles are angles greater than \[{90^ \circ }\] but less than \[{180^ \circ }\].
Reflex angles are angles greater than \[{180^ \circ }\] but less than \[{360^ \circ }\].
Angles equal to \[{360^ \circ }\], \[{180^ \circ }\] and \[{0^ \circ }\] are called straight angles.
An angle equal to \[{90^ \circ }\] is called a right angle.
Triangles can be divided into the following categories based on the length of their sides: Equilateral triangle: All three sides are equal.
Isosceles triangle: Any two of its sides are equal.
Scalene triangle: All three sides are of different lengths.
An acute angle does not include the angle equal to \[{90^ \circ }\], the angle must be less than that.