Question
In the given figure, prove that:
(i) $\triangle ABC \cong \triangle DCB$
(ii) $AC = DB$
(i) $\triangle ABC \cong \triangle DCB$
(ii) $AC = DB$
✓
Answer
Proof:
In Δ ABC and Δ DCB,
CB = CB ...........(common)
∠ABC = ∠BCD ..........(each 90°)
and AB = CD .............(given)
(i) ∴ Δ ABC ≅ Δ DCB ..............(S.A.S. Axiom)
(ii) Hence AC = DB ............(c.p.c.t.)
Hence proved.
In Δ ABC and Δ DCB,
CB = CB ...........(common)
∠ABC = ∠BCD ..........(each 90°)
and AB = CD .............(given)
(i) ∴ Δ ABC ≅ Δ DCB ..............(S.A.S. Axiom)
(ii) Hence AC = DB ............(c.p.c.t.)
Hence proved.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
88 - {5 - (- 48) ÷ (- 16)}
State the type(s) of symmetry possessed of the figure. Explain type of symmetry for these figure
Apply the properties of isosceles and equilateral triangles to find the unknown angles in the given figure:
What must be subtracted from $a^2+b^2+$ lab to get $-4 a b+2 b^2 ?$
→State, whether the pairs of triangles given in the following figures are congruent or not:
A rectangular park has length $=23 \frac{2}{3} \mathrm{~m}$ and breadth $=16 \frac{2}{3} \mathrm{~m}$. Find the area?
→Evaluate: 3.2 x 2.5 x 0.7
What must be added to $2 a^3+5 a-a^2-6$ to get $a^2-a-a^3+1$ ?
→Express the following rational numbers to the lowest terms: $\frac{14}{-56}$
→Evaluate : $3+\frac{-7}{8}+\frac{-3}{4}$
→