English

In ∆ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE. - Mathematics

Advertisements
Advertisements

Question

In ∆ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.

Sum
Advertisements

Solution

In ΔABC, we have AB = 5 cm, BC = 8 cm and CA = 7 cm.

Since, D and E are the mid-points of AB and BC, respectively.

By mid-point theorem, DE || AC

And DE = `1/2` AC = `7/2` = 3.5 cm

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Quadrilaterals - Exercise 8.2 [Page 76]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 9
Chapter 8 Quadrilaterals
Exercise 8.2 | Q 8. | Page 76

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.


Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.


ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively
intersecting at P, Q and R. Prove that the perimeter of ΔPQR is double the perimeter of
ΔABC


ABC is a triang D is a point on AB such that AD = `1/4` AB and E is a point on AC such that AE = `1/4` AC. Prove that DE = `1/4` BC.


Fill in the blank to make the following statement correct

The triangle formed by joining the mid-points of the sides of an isosceles triangle is         


In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P.
Prove that:
(i) BP = 2AD
(ii) O is the mid-point of AP.


Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.


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: 4CR = AB.


ABCD is a kite in which BC = CD, AB = AD. E, F and G are the mid-points of CD, BC and AB respectively. Prove that: The line drawn through G and parallel to FE and bisects DA.


In AABC, D and E are two points on the side AB such that AD = DE = EB. Through D and E, lines are drawn parallel to BC which meet the side AC at points F and G respectively. Through F and G, lines are drawn parallel to AB which meet the side BC at points M and N respectively. Prove that BM = MN = NC.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×