Question
Identify the type of triangle if altitudes AD, BE and CF are equal.
- Right-angled triangle
- Obtuse triangle
- Equilateral triangle
- Scalene triangle
Hint:
In geometry, an equilateral triangle is a triangle in which all three sides have the same length.
The correct answer is: Equilateral triangle
From figure, in ΔBEC and ΔBFC,
BC = BC (Common)
BE = CF (given)
∠BEC = ∠BFC = 90°
⇒ ΔBEC ≅ ΔBFC (RHS congruence criterion)
⇒∠EBC = ∠FCB (Corresponding parts of congruent triangles)
⇒ AB = AC ———-(i) (Sides opposite to equal angles are equal)
Similarly, ΔABD ≅ ΔABE by RHS congruence criterion
⇒∠DBA = ∠DAB (Corresponding parts of congruent triangles)
⇒ AB = BC ———-(ii) (Sides opposite to equal angles are equal)
From equation i and ii, AB = BC = AC ⇒ ABC is an equilateral triangle .
Hence the correct option is (a).
BC = BC (Common)
BE = CF (given)
∠BEC = ∠BFC = 90°
⇒ ΔBEC ≅ ΔBFC (RHS congruence criterion)
⇒∠EBC = ∠FCB (Corresponding parts of congruent triangles)
⇒ AB = AC ———-(i) (Sides opposite to equal angles are equal)
Similarly, ΔABD ≅ ΔABE by RHS congruence criterion
⇒∠DBA = ∠DAB (Corresponding parts of congruent triangles)
⇒ AB = BC ———-(ii) (Sides opposite to equal angles are equal)
From equation i and ii, AB = BC = AC ⇒ ABC is an equilateral triangle .
An equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.
Related Questions to study
A translation is a transformation
A translation is a transformation
From the diagram given below, we can say that ΔABC and ΔPQR are ________.
Hence Congruennt is perfect option
From the diagram given below, we can say that ΔABC and ΔPQR are ________.
Hence Congruennt is perfect option
Which of the following alphabets has a horizontal line of symmetry?
Hence All of These is the suitable option.
Which of the following alphabets has a horizontal line of symmetry?
Hence All of These is the suitable option.
A translation function is defined by the rule (x, y) → (x + 2, y - 5).
Which choice will be the image of the point (3, 6) under this translation?
In this question, we used the concept of translation and found out the points according to the condition given. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. The algebraic representation will be: (5, 1).
A translation function is defined by the rule (x, y) → (x + 2, y - 5).
Which choice will be the image of the point (3, 6) under this translation?
In this question, we used the concept of translation and found out the points according to the condition given. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. The algebraic representation will be: (5, 1).
Which of the following figures has multiple lines of symmetry (more than one line of symmetry)?
If a line can be drawn separating a figure into two identical pieces, the figure possesses line symmetry. The path is known as a symmetry line. A figure might only contain one line of symmetry, two lines of symmetry, or none at all. So here the figure 4 has more than 1 line of symmetry.
Which of the following figures has multiple lines of symmetry (more than one line of symmetry)?
If a line can be drawn separating a figure into two identical pieces, the figure possesses line symmetry. The path is known as a symmetry line. A figure might only contain one line of symmetry, two lines of symmetry, or none at all. So here the figure 4 has more than 1 line of symmetry.
The result of a translation is _______.
In this question, we used the concept of translation and found out that its an image that is formed after translation. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. Translation is changing of position of the image.
The result of a translation is _______.
In this question, we used the concept of translation and found out that its an image that is formed after translation. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. Translation is changing of position of the image.
Which of the following alphabets has no line of symmetry?
Hence P has no line of symmetry.
Which of the following alphabets has no line of symmetry?
Hence P has no line of symmetry.
A translation of (x, y) → (x + 4, y - 3) is applied to Δ PQR.P (-3, 3), Q (2, 7), R (7, 2). The coordinate of P’ is
The required point has been calculated with the given equation.
A translation of (x, y) → (x + 4, y - 3) is applied to Δ PQR.P (-3, 3), Q (2, 7), R (7, 2). The coordinate of P’ is
The required point has been calculated with the given equation.
Translation is possible
Translation is possible both vertical and horizontal.
Translation is possible
Translation is possible both vertical and horizontal.
Find the value of ∠ABD if AB = AC and DB = DC
Find the value of ∠ABD if AB = AC and DB = DC
Which of the following relation is correct?
Which of the following relation is correct?
Which of the following figures has only two lines of symmetry?
Hence option C is the correcct option
Which of the following figures has only two lines of symmetry?
Hence option C is the correcct option
From the given diagram, what can be said about sides AC and PC?
From the given diagram, what can be said about sides AC and PC?
An algebraic representation of translation of a point 6 units to the right and 3 units up
Hence option A (x+6,y+3) is the suitable option.
An algebraic representation of translation of a point 6 units to the right and 3 units up
Hence option A (x+6,y+3) is the suitable option.
Which of the following relation is correct if PQ = PS, PR = PT and ∠QPS = ∠TPR?
Which of the following relation is correct if PQ = PS, PR = PT and ∠QPS = ∠TPR?
