from a handpicked tutor in LIVE 1-to-1 classes
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that
i) △ ABD ≅ △ BAC (ii) BD = AC (iii) ∠ABD = ∠BAC.
Given: AD = BC and ∠DAB = ∠CBA
To Prove: i) △ ABD ≅ △ BAC ii) BD = AC iii) ∠ABD = ∠BAC
(i) In △ABD and △BAC,
AD = BC (Given)
∠DAB = ∠CBA (Given)
AB = BA (Common)
∴ △ABD ≅ △BAC (By SAS congruence rule)
(ii) Since △ABD ≅ △BAC,
∴ BD = AC (By CPCT)
(iii) Since △ABD ≅ △BAC,
∠ABD = ∠BAC (By CPCT)
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that i) △ ABD ≅ △ BAC ii) BD = AC iii) ∠ABD = ∠BAC
NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.1 Question 2
If ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA, then ΔABD ≅ ΔBAC using SAS congruence criteria which implies BD = AC, and ∠ABD = ∠BAC.
☛ Related Questions:
- In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure).Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?
- AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.
- l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that ΔABC ≅ ΔCDA.
- Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:i) ΔAPB ≅ ΔAQBii) BP = BQ or B is equidistant from the arms of ∠A