Question
Prove that an equilateral triangle is equiangular.
✓
Answer
Given: ∆ABC is an equilateral triangle.
To prove: ∆ABC is equiangular
i.e. ∠A ≅ ∠B ≅ ∠C …(i) [Sides of an equilateral triangle]
In ∆ABC,
seg AB ≅ seg BC [From (i)]
∴ ∠C = ∠A (ii) [Isosceles triangle theorem]
In ∆ABC,
seg BC ≅ seg AC [From (i)]
∴ ∠A ≅ ∠B (iii) [Isosceles triangle theorem]
∴ ∠A ≅ ∠B ≅ ∠C [From (ii) and (iii)]
∴ ∆ABC is equiangular.
To prove: ∆ABC is equiangular
i.e. ∠A ≅ ∠B ≅ ∠C …(i) [Sides of an equilateral triangle]
In ∆ABC,
seg AB ≅ seg BC [From (i)]
∴ ∠C = ∠A (ii) [Isosceles triangle theorem]
In ∆ABC,
seg BC ≅ seg AC [From (i)]
∴ ∠A ≅ ∠B (iii) [Isosceles triangle theorem]
∴ ∠A ≅ ∠B ≅ ∠C [From (ii) and (iii)]
∴ ∆ABC is equiangular.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following table:
Find the probability that a student chosen at random:
|
Opinion
|
Like
|
Dislike
|
|
Number of students
|
135
|
65
|
- Likes Mathematics
- Does not like it.
If $3^{x-1}=9$ and $4^{y+2}=64$, what is the value of $\frac{x}{y}$ ?
→In the given figure, y = 108° and x = 71°. Are the lines m and n parallel? Justify?
Write the following statements in ‘if-then’ form.
i. The opposite angles of a parallelogram are congruent.
ii. The diagonals of a rectangle are congruent.
iii. In an isosceles triangle, the segment joining the vertex and the midpoint of the base is perpendicular to the base.
i. The opposite angles of a parallelogram are congruent.
ii. The diagonals of a rectangle are congruent.
iii. In an isosceles triangle, the segment joining the vertex and the midpoint of the base is perpendicular to the base.
In the adjoining figure, if seg PR ≅ seg PQ, show that seg PS > seg PQ.
The percentage of marks obtained by a student in the monthly unit tests are given below:
Find the probability that the student gets:
|
Unit Test
|
I
|
II
|
III
|
IV
|
V
|
|
Percentage of Mark Obtained
|
69
|
71
|
73
|
68
|
76
|
- More than 70% marks.
- Less than 70% marks.
- A distinction
It being given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{10}=3.162,$ find the value of three places of decimals, of the following:
$\frac{2}{\sqrt{5}}$
→$\frac{2}{\sqrt{5}}$
On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that $\angle\text{BAC}=\angle\text{BDC}.$
→In the following determine rational numbers a and b:$\frac{4+\sqrt2}{2+\sqrt2}=\text{a}-\sqrt{\text{b}}$
→If$ x = 1$ and $y = 6$ is a solution of the equation $8x - ay + a^2 = 0$, find the values of a
→