Advertisements
Advertisements
प्रश्न
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
उत्तर
Given: ABCD is a quadrilateral in which AB = BC and AD = CD.
To show: BD bisects both the angles ABC and ADC.
Proof: Since, AB = BC ...(Given)
∴ ∠2 = ∠1 ...(i) [Angles opposite to equal sides are equal]
And AD = CD ...[Given]
⇒ ∠4 = ∠3 ...(ii) [Angles opposite to equal sides are equal]
On adding equations (i) and (ii), we get
∠2 + ∠4 = ∠1 + ∠3
⇒ ∠BCD = ∠BAD ...(iii)
In ΔBAD and ΔBCD,
AB = BC ...[Given]
∠BAD = ∠BCD ...[From equation (iii)]
And AD = CD ...[Given]
∴ ΔBAD ≅ ΔBCD ...[By SAS congruence rule]
Hence, ∠ABD = ∠CBD and ∠ADB = ∠CDB i.e., BD bisects the angles ABC and ADC. ...[By CPCT]
APPEARS IN
संबंधित प्रश्न
If ΔPQR≅ ΔEFD, then ∠E =
In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that:
- ∠CAD = ∠BAE
- CD = BE
The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: ΔAMC≅ ΔANB
State, whether the pairs of triangles given in the following figures are congruent or not:
State, whether the pairs of triangles given in the following figures are congruent or not:
Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.
Prove that:
- ∆ ABD ≅ ∆ ACD
- ∠B = ∠C
- ∠ADB = ∠ADC
- ∠ADB = 90°
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).
Which of the following rule is not sufficient to verify the congruency of two triangles
