Mathematics
In the given figure, AB || CD || EF and E is the mid-point of side AD, then :
OE : OF = 1 : 3
OE = OF
OF = 2 x OE
CF = FB
Answer
Given,
E is mid-point of AD.
Since, EF || DC ⇒ EO || DC
According to converse of the mid-point theorem, in any triangle, a straight line through the midpoint of one side that is parallel to a second side, then that line bisects the third side.
⇒ OA = OC
⇒ O is the mid-point of AC.
Since, EF || AB ⇒ OF || AB
According to converse of the mid-point theorem,
F will be the mif-point of BC.
⇒ CF = FB
Hence, option 4 is the correct option.
Related Questions
The midpoint of the side of a triangle are joined together to get four triangles. These four triangles are:
not equal to each other
congruent to each other
not congruent to each other
none of these
In the given figure, AB || CD || EF. If AC = 7 cm, AE = 14 cm and BF = 20 cm, then DF is equal to:
7 cm
14 cm
10 cm
16 cm
In rhombus PQRS; A, B and C are mid-points of sides PQ, QR and RS respectively. If ∠P = 60°, the angle PQR is equal to:
60°
90°
120°
none of these
Statement 1: The diagonals of a quadrilateral are perpendicular to each other; P, Q, R and S are the midpoints of sides AB, BC, CD and DA respectively.
Statement 2: Quadrilateral PQRS is a square.
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.