English

In δAbc, D, E, F Are the Midpoints of Bc, Ca and Ab Respectively. Find Fe, If Bc = 14 Cm - Mathematics

Advertisements
Advertisements

Question

In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find FE, if BC = 14 cm

Sum
Advertisements

Solution


F is the mid-point AB and E is the mid-point of AC.
∴ FE = `(1)/(2)"BC"`       ....(Mid-point Theorem)

= `(1)/(2) xx 14`
= 7 cm.

shaalaa.com
  Is there an error in this question or solution?
Chapter 15: Mid-point and Intercept Theorems - Exercise 15.1

APPEARS IN

Frank Mathematics [English] Class 9 ICSE
Chapter 15 Mid-point and Intercept Theorems
Exercise 15.1 | Q 3.1

RELATED QUESTIONS

In Fig. below, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are
respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°.


ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the
mid-points of the sides, in order, is a rectangle.


In the adjacent figure, `square`ABCD is a trapezium AB || DC. Points M and N are midpoints of diagonal AC and DB respectively then prove that MN || AB.


The side AC of a triangle ABC is produced to point E so that CE = AC. D is the mid-point of BC and ED produced meets AB at F. Lines through D and C are drawn parallel to AB which meet AC at point P and EF at point R respectively.

Prove that:

  1. 3DF = EF
  2. 4CR = AB

In trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC.
Prove that: AB + DC = 2EF.


In ΔABC, P is the mid-point of BC. A line through P and parallel to CA meets AB at point Q, and a line through Q and parallel to BC meets median AP at point R. Prove that: AP = 2AR


Side AC of a ABC is produced to point E so that CE = `(1)/(2)"AC"`. D is the mid-point of BC and ED produced meets AB at F. Lines through D and C are drawn parallel to AB which meets AC at point P and EF at point R respectively. Prove that: 3DF = EF


In the given figure, PS = 3RS. M is the midpoint of QR. If TR || MN || QP, then prove that:

ST = `(1)/(3)"LS"`


The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if ______.


D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×