Advertisements
Advertisements
प्रश्न
The vertical angle of an isosceles triangle is 100°. Find its base angles.
Advertisements
उत्तर
Consider an isosceles ΔABC such that AB= AC
Given that vertical angle A is 100°. Given to find the base angles
SinceΔABC is isosceles
∠B = ∠C [Angles opposite to equal angle are equal]
And also ,
Sum of the interior angle of a triangle = 180°
⇒∠Aa+∠B+∠C=180°
⇒100°+∠B+∠B=180°
⇒2∠B=180°-100° ⇒2∠B=80°
⇒∠B=40 °
⇒∠B=∠C=40°
APPEARS IN
संबंधित प्रश्न
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Which of the following statements are true (T) and which are false (F):
The bisectors of two equal angles of a triangle are equal
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Write the sum of the angles of an obtuse triangle.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, what is the value of x?
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
Which of the following correctly describes the given triangle?
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
