Home
Class 9
MATHS
Theorem 6.8 : If a side of a triangle is...

Theorem 6.8 : If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Text Solution

AI Generated Solution

To prove Theorem 6.8, which states that if a side of a triangle is produced, then the exterior angle formed is equal to the sum of the two interior opposite angles, we can follow these steps: ### Step-by-Step Solution: 1. **Draw Triangle and Extend a Side**: - Let triangle ABC be given, and extend side BC to a point D. - This creates an exterior angle ∠ACD. ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Exterior angle theorem: If a side of a triangle is produced; the exterior angle so formed is equal to the sum of the two interior opposite angles.

(Exterior Angle Theorem): If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. GIVEN : A triangle A B CdotD is a point of B C produced, forming exterior angle /_4. TO PROVE : /_4=/_1+/_2 i.e. , /_A C D=/_C A B+/_C B Adot

Knowledge Check

  • one side of a triangle is produced and the exterior angle so formed is 140^@ . If the interior opposite angles are in the ratio. 2:5, find the measure of each angle of the triangle.

    A
    `40^@, 75^@, 60^@`
    B
    `40^@, 70^@, 70^@`
    C
    `40^@, 100^@, 40^@`
    D
    `40^@, 75^@, 65^@`

    • Similar Questions

    Explore conceptually related problems

    THEOREM (Exterior Angle Property of a Triangle): If a side of a triangle is produced the exterior angle so formed is equal to the sum of two interior opposite angles.

    27.Prove that an exterior angle of a triangle is equal to the sum of its interior opposite angles.

    If one side of a cyclic quadrilateral is produced,then the exterior angle is equal to the interior opposite angle.

    If one side of a cyclic quadrilateral is produced; then the exterior angle is equal to the interior opposite angle.

    If a side of the cyclic quadrlateral is produced ; then the external angle is equal to the interior opposite angles.

    one side of a triangle is produced and the exterior angle so formed is 120^(@) .if the interior opposite angles be in the ratio 3:5 .find the measure of each angles of triangle .

    The measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles

    Home
    Profile