English

In δAbc, D, E, F Are the Midpoints of Bc, Ca and Ab Respectively. Find De, If Ab = 8 Cm

Advertisements
Advertisements

Question

In ΔABC, D, E, F are the midpoints of BC, CA and AB respectively. Find DE, if AB = 8 cm

Sum
Advertisements

Solution


D is the mid-point BC and E is the mid-point of AC.

∴ DE = `(1)/(2)"AB"`      ....(Mid-point Theorem)

= `(1)/(2) xx 8`
= 4 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 3.2

RELATED QUESTIONS

In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC =
21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.


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.


The following figure shows a trapezium ABCD in which AB // DC. P is the mid-point of AD and PR // AB. Prove that:

PR = `[1]/[2]` ( AB + CD)


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, AB = 12 cm and AC = 9 cm. If M is the mid-point of AB and a straight line through M parallel to AC cuts BC in N, what is the length of MN?


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


In parallelogram ABCD, P is the mid-point of DC. Q is a point on AC such that CQ = `(1)/(4)"AC"`. PQ produced meets BC at R. Prove that

(i) R is the mid-point of BC, and

(ii) PR = `(1)/(2)"DB"`.


In a parallelogram ABCD, M is the mid-point AC. X and Y are the points on AB and DC respectively such that AX = CY. Prove that:
(i) Triangle AXM is congruent to triangle CYM, and

(ii) XMY is a straight line.


In a parallelogram ABCD, E and F are the midpoints of the sides AB and CD respectively. The line segments AF and BF meet the line segments DE and CE at points G and H respectively Prove that: EGFH is a parallelogram.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×