Mathematics
Consider the following two statements:
Statement 1: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.
Statement 2: The line through the mid-point of one side of a triangle and parallel to another side bisects the third side.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Mid-point Theorem
2 Likes
Answer
According to statement 1 :
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.
This statement describes mid-point theorem.
∴ Statement 1 is true.
According to statement 2 :
The line through the mid-point of one side of a triangle and parallel to another side bisects the third side.
This statement describes the converse of mid-point theorem.
∴ Statement 2 is true.
Hence, option 1 is the correct option.
Answered By
1 Like
Related Questions
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order is a rhombus if
ABCD is a parallelogram
ABCD is a rhombus
the diagonals of ABCD are equal
the diagonals of ABCD are perpendicular to each other.
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if
ABCD is a rhombus
diagonals of ABCD are equal
diagonals of ABCD are perpendicular to each other
diagonals of ABCD are equal and perpendicular to each other.
Assertion (A): For a Δ ABC, line segment EF is drawn such that E is the midpoint of AB and F is a midpoint of AC. Then the quadrilateral formed EFCB is a trapezium.
Reason (R): The line segment joining the midpoint of two sides of a triangle is parallel to the third side.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Assertion (A): In a Δ DEF, we have DE = EF = DF = 6 cm. A line segment PQ is drawn parallel to DF such that EP = 3 cm. Then we can conclude that PQ = 3 cm.
Reason (R): Any line segment drawn inside a triangle parallel to the base of the triangle cuts the removing two sides in half.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).