Advertisements
Advertisements
प्रश्न
ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.
Advertisements
उत्तर
In the triangle ABC it is given that
AB = AC, BE and CFare medians.
We have to show that BE CF
To show BF = CF we will show that ΔBFC ≅ ΔBEC
In triangle ΔBFC and ΔBEC
As AB = AC, so
∠FBC = ∠ECF .........(1)
BC=BC (common sides) ........(2)
Since,
AB = AC
`1/2 AB =1/2 AC `
As F and E are mid points of sides AB and AC respectively, so
BF = CE ..........(3)
From equation (1), (2), and (3)
ΔBFC and ΔBEC
Hence FC = BE Proved.
APPEARS IN
संबंधित प्रश्न
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that
- ΔABD ≅ ΔBAC
- BD = AC
- ∠ABD = ∠BAC.
You want to show that ΔART ≅ ΔPEN,
If it is given that AT = PN and you are to use ASA criterion, you need to have
1) ?
2) ?
If perpendiculars from any point within an angle on its arms are congruent, prove that it lies on the bisector of that angle.
In Fig. 10.99, AD ⊥ CD and CB ⊥. CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP.
In Δ ABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in P. Arrange AP, BP and CP in descending order.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent.
(ii) AB = CE.
(iii) AB is parallel to EC
AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.
In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.
Prove that : (i) BO = CO
(ii) AO bisects angle BAC.
In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced up to point R so that CR = BP.
Prove that QR bisects PC.
Hint: ( Show that ∆ QBP is equilateral
⇒ BP = PQ, but BP = CR
⇒ PQ = CR ⇒ ∆ QPM ≅ ∆ RCM ).
PQRS is a parallelogram. L and M are points on PQ and SR respectively such that PL = MR.
Show that LM and QS bisect each other.
