Advertisements
Advertisements
Question
If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.
Advertisements
Solution
Given each angle of a triangle less than the sum of the other two
`∴∠A+∠ B+∠C`
`⇒∠A+∠A<∠A+∠B+∠C`
`⇒2∠A<180^@`
[Sum of all angles of a triangle]
`⇒∠A<90^@`
Similarly` ∠ B< 90^@ and ∠C<90^@`
Hence, the triangles acute angled.
APPEARS IN
RELATED QUESTIONS
If the angles of a triangle are in the ratio 1: 2 : 3, determine three angles.
If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.
In the given figure, AB || DE. Find ∠ACD.
Is the following statement true and false :
A triangle can have at most one obtuse angles.
Is the following statement true and false :
If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
One angle of a triangle is 60°. The other two angles are in the ratio of 5: 7. Find the two angles.
Classify the following triangle according to angle:
The angles of the triangle are 3x – 40, x + 20 and 2x – 10 then the value of x is
Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC = ∠ABC.
The number of triangles in the following figure is ______. Their names are ______.
