Advertisements
Advertisements
प्रश्न
In the given figure: AB//FD, AC//GE and BD = CE;
prove that:
- BG = DF
- CF = EG
Advertisements
उत्तर
In the given figure AB || FD,
⇒ ∠ABC =∠FDC
Also AC || GE,
⇒ ∠ACB = ∠GEB
Consider the two triangles ΔGBE and ΔFDC
∠B = ∠D ...(Corresponding angle)
∠C = ∠E ...(Corresponding angle)
Also given that
BD = CE
⇒ BD + DE = CE + DE
⇒ BE = DC
∴ By Angle-Side-Side-Angle criterion of congruence
ΔGBE ≅ ΔFDC
∴ `"GB"/"FD" = "BE"/"DC" = "GE"/"FC"`
But BE = DC
⇒ `"BE"/"DC" = "BE"/"BE"` = 1
∴ `"GB"/"FD" = "BE"/"DC"` = 1
⇒ GB = FD
∴ `"GE"/"FC" = "BE"/"DC"` = 1
⇒ GE = FC
APPEARS IN
संबंधित प्रश्न
You want to show that ΔART ≅ ΔPEN,
If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
1) RT = and
2) PN =
In the figure, the two triangles are congruent.
The corresponding parts are marked. We can write ΔRAT ≅ ?
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
In triangles ABC and CDE, if AC = CE, BC = CD, ∠A = 60°, ∠C = 30° and ∠D = 90°. Are two triangles congruent?
In the given figure, ABC is an isosceles triangle whose side AC is produced to E. Through C, CD is drawn parallel to BA. The value of x is
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB = CE.
From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.
Prove that:
(i) ΔDCE ≅ ΔLBE
(ii) AB = BL.
(iii) AL = 2DC
In the following figure, BL = CM.
Prove that AD is a median of triangle ABC.
In the following diagram, AP and BQ are equal and parallel to each other. 
Prove that: AB and PQ bisect each other.
