Advertisements
Advertisements
प्रश्न
In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?
Advertisements
उत्तर
Given: In quadrilateral ABCD, AC = AD and AB bisects ∠A.
To prove: △ABC ≌ △ABD
Proof: In △ABC and △ABD,
AC = AD ...[Given]
∠BAC = ∠BAD ...[∵ AB bisects ∠A]
AB = AB ...[Common]
∴ △ABC ≌ △ABD ...[By SAS congruence rule]
Hence, BC = BD ...[Corresponding parts of congruent triangles]
APPEARS IN
संबंधित प्रश्न
AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.
In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
In the figure, the two triangles are congruent.
The corresponding parts are marked. We can write ΔRAT ≅ ?
Explain, why ΔABC ≅ ΔFED.
In triangles ABC and CDE, if AC = CE, BC = CD, ∠A = 60°, ∠C = 30° and ∠D = 90°. Are two triangles congruent?
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB = CE.
A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that: QA = QB.
In the given figure, AB = DB and Ac = DC.
If ∠ ABD = 58o,
∠ DBC = (2x - 4)o,
∠ ACB = y + 15o and
∠ DCB = 63o ; find the values of x and y.
In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that: BD = CD
Which of the following is not a criterion for congruence of triangles?
