Home
Class 10
MATHS
The external angle bisector of an angle ...

The external angle bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

Text Solution

AI Generated Solution

To prove that the external angle bisector of an angle in a triangle divides the opposite side externally in the ratio of the sides containing the angle, we can follow these steps: ### Step-by-Step Solution: 1. **Consider Triangle ABC**: Let triangle ABC have angle A at vertex A. Let AD be the external angle bisector of angle A, meeting the line extended from BC at point D. 2. **Label the Sides**: Let the lengths of sides opposite to vertices A, B, and C be denoted as a, b, and c respectively. Specifically, let: - \( AB = c \) ...
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/ Exemplar|14 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6a|24 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|4 Videos

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revisions Exercise Long Answer Questions|5 Videos

Similar Questions

Explore conceptually related problems

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

One exterior angle of a triangle is 70^(@) . The two opposite interior angles are in the ratio 2:5. find the angles of the triangle.

One angle of a triangle is equal to one angle of another triangle and the bisectors of these two equal angles divide the opposite sides in the same ratio, prove that the triangles are similar.

One exterior angle of a triangle is 110^(@) . Two two opposite interior angles are in the ratio 5:6. find the angles of the triangle.

Prove that the internal bisector of the angle A of a triangle ABC divides BC in the ratio AB:AC

The exterior angles of a triangle is 130^(@) and the two interior opposite angle are in the ratio 6:7. find the angles of the triangle.

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

In a DeltaABC, the tangent of hald the difference of two angle is one-third the tangent of half the sum of the angle. Determine the ratio of the sides opposite to the angles.

In a Delta ABC the tangent of half the difference of two angles is one thired the tangement of half the sum of the angles .Determine the ratio of the sides opposite to the angles .