हिंदी

Use the Following Figure to Find: Bc, If Ab = 7.2 Cm Ge, If Fe = 4 Cm Ae, If Bd = 4.1 Cm (Iv) Df, If Cg = 11 Cm - Mathematics

Advertisements
Advertisements

प्रश्न

Use the following figure to find:
(i) BC, if AB = 7.2 cm.
(ii) GE, if FE = 4 cm.
(iii) AE, if BD = 4.1 cm
(iv) DF, if CG = 11 cm.

योग
Advertisements

उत्तर

According to the equal intercept theorem since CD = DE
Therefore AB = BC and EF = GF

(i) BC = AB = 7.2cm

(ii) GE = EF + GF

= 2EF

= 2 x 4

=8cm

Since B, D, and F are the mid-point and AE || BF || CG
Therefore AE = 2BD and CG = 2DF

(iii) AE = 2BD

= 2 x 4.1

= 8.2

(iv) DF = `[1]/[2]`CG

= `[1]/[2]` x 11

= 5.5 cm

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Mid-point and Its Converse [ Including Intercept Theorem] - Exercise 12 (B) [पृष्ठ १५३]

APPEARS IN

सेलिना Concise Mathematics [English] Class 9 ICSE
अध्याय 12 Mid-point and Its Converse [ Including Intercept Theorem]
Exercise 12 (B) | Q 1 | पृष्ठ १५३

संबंधित प्रश्न

In below fig. ABCD is a parallelogram and E is the mid-point of side B If DE and AB when produced meet at F, prove that AF = 2AB.


In a ∆ABC, D, E and F are, respectively, the mid-points of BC, CA and AB. If the lengths of side AB, BC and CA are 7 cm, 8 cm and 9 cm, respectively, find the perimeter of ∆DEF.


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


Fill in the blank to make the following statement correct:

The triangle formed by joining the mid-points of the sides of a right triangle is            


In trapezium ABCD, AB is parallel to DC; P and Q are the mid-points of AD and BC respectively. BP produced meets CD produced at point E.

Prove that:

  1. Point P bisects BE,
  2. PQ is parallel to 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

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles ΔABC in which AB = BC. Prove that ΔDEF is also isosceles.


If L and M are the mid-points of AB, and DC respectively of parallelogram ABCD. Prove that segment DL and BM trisect diagonal AC.


ΔABC is an isosceles triangle with AB = AC. D, E and F are the mid-points of BC, AB and AC respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.


E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = `1/3` AC.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×