Question

Fill in the blank with the correct word/symbol to make it a true statement.
A triangle with all the angles are of measure less than $90^\circ $ is known as ______.

Answer 1

Hint: Triangles are categorized different ways based on sides and angles. According to angles there are three categories; that are less than ${90^ \circ }$ angle, greater than ${90^ \circ }$angle and equal to ${90^ \circ }$angle.

Useful formula:
Triangle is a polygon with three sides and three angles.
Therefore the sum of interior angles is $(n - 2)180 = (3 - 2)180 = 180$.

Complete step by step solution:
We are asked the name of the triangles with every angle less than ${90^ \circ }$.
If every angle in a triangle is less than ${90^ \circ }$, such triangles are known as Acute triangles.
And if any of the three angles is greater than ${90^ \circ }$, such triangles are called Obtuse triangles.
If one of the angles of the triangle is equal to ${90^ \circ }$, such triangle is called Right angled triangle.

Additional information:
If an angle of a triangle is acute ($ < {90^ \circ }$), then the exterior angle at that vertex will be obtuse ($ > {90^ \circ }$), since these two make a linear pair.
An exterior angle of a vertex of a triangle is equal to the sum of the interior angles of the other two vertices.

Note:For an acute triangle the orthocentre (intersection of the altitudes) and circumcentre (intersection of side bisectors) lie inside the circle. But in case of obtuse triangles these two lie outside the triangle.
The incentre ( intersection of angle bisectors) and centroid (intersection of medians) lie inside the circle for every triangle.