Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given in the question, bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Now BO is produced to a point M.
In triangle ABC,
AB = AC
∠ABC = ∠ACB ...[Angle opposite to equal sides of a triangle are equal]
`1/2 ∠ABC = 1/2 ∠ACB`
That is ∠1 = ∠2 ...[Since, BO and CO are bisectors of ∠B and ∠C]
In triangle OBC,
Exterior ∠MOC = ∠1 + ∠2 ...[Exterior angle of a triangle is equal to the sum of interior opposite angles]
Exterior ∠MOC = 2∠1 ...[∠1 = ∠2]
Hence, ∠MOC = ∠ABC.
APPEARS IN
संबंधित प्रश्न
In a ΔABC, if ∠A = 55°, ∠B = 40°, find ∠C.
In a ΔABC, ∠ABC = ∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Show that ∠A = ∠B = ∠C = 60°.
Is the following statement true and false :
A triangle can have at most one obtuse angles.
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
If two sides of a triangle are 5 cm and 1.5 cm, the length of its third side cannot be ______.
Find the unknown marked angles in the given figure:
The length of the sides of the triangle is given. Say what types of triangles they are 4.3 cm, 4.3 cm, 4.3 cm.
One of the angles of a triangle is 65°. If the difference of the other two angles is 45°, then the two angles are
What is common in the following figure?
 |
 |
| (i) | (ii) |
Is figure (i) that of triangle? if not, why?
What is the sum of the measures of the interior angles of any triangle, △ABC?
