Advertisements
Advertisements
प्रश्न
In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR.
Prove that ΔABC and ΔPQR are congruent.
 |
 |
Advertisements
उत्तर
Given: AB = PQ ; BC = QR ; AD = PS
To prove: ΔABC ≅ ΔPQR
Proof:
BC = QR
2 BD = 2 QS
BD = QS ...(i)
In Δ ABD and Δ PQS
AB = PQ ...[Given]
BD = QS ...[From equation (i)]
AD = PS ...[Given]
∴ ΔABD ≅ ΔPQS ...[by SSS rule]
Then, ∠B = ∠Q ...[by CPCTC] ...(ii)
In ΔABC and ΔPQR
AB = PQ ...[Given]
∠B = ∠Q ...[ii]
BC = QR ...[Given]
∴ ΔABC ≅ ΔPQR ...[by SAS rule]
Hence proved.
APPEARS IN
संबंधित प्रश्न
In Δ ABC, ∠B = 35°, ∠C = 65° and the bisector of ∠BAC meets BC in P. Arrange AP, BP and CP in descending order.
D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle
If the following pair of the triangle is congruent? state the condition of congruency :
In Δ ABC and Δ DEF, AB = DE, BC = EF and ∠ B = ∠ E.
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from B and C to the opposite sides are equal.
From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.
prove that : AL = 2DC
In ∆ABC, AB = AC. Show that the altitude AD is median also.
ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such produced to E and F respectively, such that AB = BE and AD = DF.
Prove that: ΔBEC ≅ ΔDCF.
In the following diagram, ABCD is a square and APB is an equilateral triangle.
- Prove that: ΔAPD ≅ ΔBPC
- Find the angles of ΔDPC.
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 ).
