Advertisements
Advertisements
Question
Prove that each angle of an equilateral triangle is 60°.
Advertisements
Solution
Given to prove that each angle of an equilateral triangle is 60°
Let us consider an equilateral triangle ABC
Such that AB= BC= CA
Now,
AB=BC ⇒ ∠A=∠C ................(1) [Opposite angles to equal sides are equal]
and BC = AC ⇒∠B = ∠A ……..(2)
From (1) and (2), we get
∠A = ∠B = ∠C ..............(3)
We know that
Sum of angles in a triangle =180°
⇒∠A+∠B+∠C=180°
⇒ ∠A+∠A+∠A=180°
⇒3 ∠A=180°
⇒ `∠A=(180°)/3=60°`
∴∠S=∠B=∠C=60°
Hence, each angle of an equilateral triangle is 60°.
APPEARS IN
RELATED QUESTIONS
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
- ΔABE ≅ ΔACF
- AB = AC, i.e., ABC is an isosceles triangle.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
Find the measure of each exterior angle of an equilateral triangle.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, x + y =
In the given figure, what is z in terms of x and y?
The angles of a right angled triangle are
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
In ∆PQR, if ∠R > ∠Q, then ______.
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.
Find all the angles of an equilateral triangle.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
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.
