Home
Class 9
MATHS
Theorem 7.3 : The sides opposite to equa...

Theorem 7.3 : The sides opposite to equal angles of a triangle are equal.

Text Solution

Verified by Experts


In `/_\BAD` and `/_\CAD`
`/_B=/_C` (given)
`/_BAD=/_CAD`
`AD=AD` (common)
By AAS congruence rule, `/_\BAD`and `/_\CAD` are congruent. Thus,
`AB=AC`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Angles opposite to two equal sides of a triangle are equal.

Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

Knowledge Check

  • The side opposite to an obtuse angle of a triangle is :

    A
    smallest
    B
    greatest
    C
    half of the perimeter
    D
    none of these

  • Which of the following is false? (A) The sum of any two sides of a triangle is equal to the third side. (B) The sum of the exterior angles of a triangle is equal to 360^(@)

    A
    A and B
    B
    Only A
    C
    Only B
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    Fill in the blanks in the following so that each of the following statements is true Sides opposite to equal angles of a triangle are ....... Angle opposite to equal sides of a triangle are ....... In an opposite to equal sides of a triangle are ....... In a A B C if /_A=/_C , then A B= ..... If altitudes C E a n d B F of a triangle A B C are equal, then A B= ........ In an isosceles triangle A B C with A B=A C , if B D a n d C E are its altitudes, then B D is .......... C E In right triangles A B C a n d D E F , if hypotenuse A B=E F and side A C=D E , then A B C ~= ....

    Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal.

    Prove that the angle opposite to the equal sides of an equilateral triangle are equal.

    Angles opposite to two equal sides of a triangle are equal. GIVEN : A B C in which A B=A C TO PROVE : /_C=/_B CONSTRUCTION : Draw the bisector A D of /_A which meets B C in D Figure

    The angles opposite to equal sides of an isosceles triangle are ..........

    If the angles of a triangle are in the ratio 2:3:7, then the sides opposite to the angles are in the ratio

    Home
    Profile