ABC is the equilateral triangle AB AC; AB is the circle of the circle BC Determine the length of the CD when BD = 4 cm
Answers
Answer:
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Answer:
. In quadrilateral ABCD we have
AC = AD
and AB being the bisector of ∠A.
Now, in ΔABC and ΔABD,
AC = AD
[Given]
AB = AB
[Common]
∠CAB = ∠DAB [∴ AB bisects ∠CAD]
∴ Using SAS criteria, we have
ΔABC ≌ ΔABD.
∴ Corresponding parts of congruent triangles (c.p.c.t) are equal.
∴ BC = BD.
2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that
(i) ΔABD ≌ ΔBAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.
Ans. (i) In quadrilateral ABCD, we have AD = BC and
∠DAB = ∠CBA.
In ΔABD and ΔBAC,
AD = BC
[Given]
AB = BA
[Common]
∠DAB = ∠CBA
[Given]
∴ Using SAS criteria, we have ΔABD ≌ ΔBAC
(ii) ∵ ΔABD ≌ ΔBAC
∴ Their corresponding parts are equal.
⇒ BD = AC
(ii) Since ΔABD ≌ ΔBAC
∴ Their corresponding parts are equal.
⇒ ∠ABD = ∠BAC.
3. AD and BC are equal perpendiculars to a line
Step-by-step explanation:
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