Mathematics
Assertion (A) : An equilateral triangle has a point of symmetry.
Reason (R) : A plane figure is said to have a point symmetry about a point, if every line segment drawn in the given figure passing through it is bisected by this point.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Symmetry
1 Like
Answer
A plane figure is said to have point symmetry about a point if every line segment drawn in the given figure passing through that point is bisected by it.
So, reason (R) is true.
A figure has point symmetry if it looks the same after being rotated 180 degrees about a central point.
If we rotate an equilateral triangle by 180°, it will not map onto itself. Thus, an equilateral triangle has no point of symmetry.
So, assertion (A) is false.
∴ A is false, but R is true.
Hence, option 4 is the correct option.
Answered By
3 Likes
Related Questions
Assertion (A) : The image of a point A(5, 6) under an anticlockwise rotation of 90°, about the origin is A'(-6, 5).
Reason (R) : When a point P is rotated through 90° clockwise direction about the origin, then abscissa of the given point becomes the ordinate with opposite sign of the resultant point and the ordinate of the given point becomes the abscissa of the resultant point.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : A shape (say circle) can be rotated from one position to another about it centre.
Reason (R) : Rotation is defined by (i)the angle of rotation, (ii) the direction of rotation and the centre of rotation.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : A parallelogram has a rotational symmetry of order 2 about the point of intersection O of its diagonals.
Reason (R) : A plane figure is said to have rotational symmetry if it aligns with the original position only once while being rotated about 360°.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are incorrect.
A is true, but R is false.
A is false, but R is true.
Construct a triangle PQR in which:
QR = 4.6cm, Q = ∠R = 50°.
Draw all its lines of symmetry.