Advertisements
Advertisements
प्रश्न
In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
Advertisements
उत्तर
Given that
∠BAD = ∠EAC
On adding ∠DAC on both sides, we get
∠BAD + ∠DAC = ∠EAC + ∠DAC
⇒ ∠BAC = ∠EAD …(I)
Now, in △ABC and △AED,
AB = AD ...[Given]
AC = AE ...[Given]
∠BAC = ∠EAD ...[By (I)]
∴ △ABC ≌ △ADE ...[By AAS congruence rule]
⇒ BC = DE ...[Corresponding parts of congruent triangles]
APPEARS IN
संबंधित प्रश्न
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
If ABC and DEF are two triangles such that AC = 2.5 cm, BC = 5 cm, ∠C = 75°, DE = 2.5 cm, DF = 5cm and ∠D = 75°. Are two triangles congruent?
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔPQR, AB = PQ, AC = PR, and BC = QR.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB is parallel to EC.
The perpendicular bisectors of the sides of a triangle ABC meet at I.
Prove that: IA = IB = IC.
From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.
Prove that: AB = BL.
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 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.
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB.
Prove that: AD = CE.
ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.
