In ΔACB and ΔADB, AC = AD [∵ Given] ∠CAB = ∠DAB [∵ AB bisects angle A] AB = AB [∵ Common] Hance, ΔABC ≅ ΔABD [∵ SAS Congruency Rule] BC = BD [∵ Corresponding parts of congruent triangles are equal]
In ΔACB and ΔADB,
AC = AD [∵ Given]
∠CAB = ∠DAB [∵ AB bisects angle A]
AB = AB [∵ Common]
Hance, ΔABC ≅ ΔABD [∵ SAS Congruency Rule]
BC = BD [∵ Corresponding parts of congruent triangles are equal]
l and m are two parallel lines intersected by another pair of parallel lines p and q (see Figure). Show that ΔABC ≅ ΔCDA.
AD and BC are equal perpendiculars to a line segment AB (see Figure). Show that CD bisects AB.
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC (iii) ∠ABD = ∠BAC.
In quadrilateral ACBD, AC = AD and AB bisects ∠A (see Figure). Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?
In quadrilateral ACBD, AC = AD and AB bisects ∠A (see Figure). Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?
In ΔACB and ΔADB, AC = AD [∵ Given] ∠CAB = ∠DAB [∵ AB bisects angle A] AB = AB [∵ Common] Hance, ΔABC ≅ ΔABD [∵ SAS Congruency Rule] BC = BD [∵ Corresponding parts of congruent triangles are equal]
In ΔACB and ΔADB,
See lessAC = AD [∵ Given]
∠CAB = ∠DAB [∵ AB bisects angle A]
AB = AB [∵ Common]
Hance, ΔABC ≅ ΔABD [∵ SAS Congruency Rule]
BC = BD [∵ Corresponding parts of congruent triangles are equal]