Advertisements
Advertisements
प्रश्न
Prove that each angle of an equilateral triangle is 60°.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
Find the measure of each exterior angle of an equilateral triangle.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
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.
The sum of any two sides of a triangle is .... than the third side.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, what is z in terms of x and y?
In the given figure, what is the value of x?
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 base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
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 ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
