Advertisements
Advertisements
प्रश्न
Show that the angles of an equilateral triangle are 60° each.
Advertisements
उत्तर
Let ABC be an equilateral triangle.
∴ AB = BC = AC …(A)
AB = BC ...[Taking first and second terms]
⇒ ∠C = ∠A …(i) ...[Angles opposite to equal sides]
Therefore,
AB = AC ...[Taking first and third terms of (A)]
⇒ ∠C = ∠B …(ii) ...[Angles opposite to equal sides]
From (i) and (ii) we get
∠A = ∠B = ∠C …(iii)
Now in △ABC …(iv)
∠A + ∠B + ∠C = 180° ...[Angle Sum Property]
⇒ ∠A + ∠A + ∠A = 180°
⇒ 3∠A = 180
⇒ ∠A = 60°
From (iii), ∠A = ∠B = ∠C
⇒ ∠A = ∠B = ∠C = 60°
Hence, each angle of an equilateral triangle is 60°.
APPEARS IN
संबंधित प्रश्न
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 Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
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 the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is z in terms of x and y?
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 =
Find all the angles of an equilateral triangle.
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
