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

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

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


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.


Let Abc Be an Isosceles Triangle in Which Ab = Ac. If D, E, F Be the Mid-points of the Sides Bc, Ca and a B Respectively, Show that the Segment Ad and Ef Bisect Each Other at Right Angles.


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.


If the quadrilateral formed by joining the mid-points of the adjacent sides of quadrilateral ABCD is a rectangle,
show that the diagonals AC and BD intersect at the right angle.


AD is a median of side BC of ABC. E is the midpoint of AD. BE is joined and produced to meet AC at F. Prove that AF: AC = 1 : 3.


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: ∠EFG = 90°


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 ΔABC, D, E and F are the midpoints of AB, BC and AC.
If AE and DF intersect at G, and M and N are the midpoints of GB and GC respectively, prove that DMNF is a parallelogram.


D, E and F are respectively the mid-points of the sides AB, BC and CA of a triangle ABC. Prove that by joining these mid-points D, E and F, the triangles ABC is divided into four congruent triangles.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×