Advertisements
Advertisements
प्रश्न
In a ΔABC, BD is the median to the side AC, BD is produced to E such that BD = DE.
Prove that: AE is parallel to BC.
Advertisements
उत्तर
Given: A(ΔABC) in which BD is the median to AC.
BD is produced to E such that BD = DE,
We need to prove that AE II BC.
Construction: Join AE
Proof:
AD = DC ...[ BD is median to AC ] ...(1)
In ΔBDC and ΔADE,
BD = DE ...[ Given ]
∠BDC = ∠ADE = 90° ...[ Vertically opposite angles ]
AD = DC ...[ from(1) ]
∴ By Side-Angle-Side Criterion of congruence,
ΔBDC ≅ ΔADE
The corresponding parts of the congruent triangles are congruent.
∴ ∠EAD = ∠BCD ...[ c.p.c.t. ]
But these are alternate angles and AC is the transversal.
Thus, AE || BC.
APPEARS IN
संबंधित प्रश्न
Which congruence criterion do you use in the following?
Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
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) ?
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
The following figure shows a circle with center O.
If OP is perpendicular to AB, prove that AP = BP.
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
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB = CE.
In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the triangle PQR.
If XS ⊥ QR and XT ⊥ PQ;
Prove that:
- ΔXTQ ≅ ΔXSQ.
- PX bisects angle P.
In the following diagram, AP and BQ are equal and parallel to each other. 
Prove that: AB and PQ bisect each other.
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 a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB.
Prove that: AD = CE.
