Advertisements
Advertisements
Question
Find all the angles of an equilateral triangle.
Advertisements
Solution
Let ABC be an equilateral triangle such that AB = BC = CA
We have, AB = AC ⇒ ∠C = ∠B ...[Angle opposite to equal sides are equal]
Let ∠C = ∠B = x° ...(i)
Now, BC = BA
⇒ ∠A = ∠C ...(ii) [Angles opposite to equal sides are equal]
From equations (i) and (ii),
∠A = ∠B = ∠C = x
Now, in ΔABC, ∠A + ∠B + ∠C = 180° ...[By angle sum property of a triangle]
⇒ x + x + x = 180°
⇒ 3x = 180°
∴ x = 60°
Hence, ∠A = ∠B = ∠C = 60°
APPEARS IN
RELATED QUESTIONS
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.
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
Show that the angles of an equilateral triangle are 60° each.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
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.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
The angles of a right angled triangle are
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.
