Download App

Congruency: Congruent Triangles — MATHS STD 7 — Question

ICSE BoardEnglish MediumSTD 7MATHSCongruency: Congruent Triangles4 Marks
Question
In the given figure, prove that:
(i) $\triangle AOD \cong \triangle BOC$
(ii) $A D=B C$
(iii) $\angle ADB =\angle ACB$
(iv) $\triangle ADB \cong \triangle BCA$
✓

Answer

Proof:
In Δ AOD and Δ BOC
OA = OB ........(given)
∠AOD = ∠BOC .............(vertically opposite angles)
OD = OC ............(given)
(i) ∴ Δ AOD ≅ Δ BOC ................(S.A.S. Axiom)
Hence (ii) AD = BC ..........(c.p.c.t.)
and (iii) ∠ADB = ∠ACB .....(c.p.c.t.)
(iv) Δ ADB ≅ Δ BCA
Δ ADB = Δ BCA ..............(Given)
AB = AB .................(Common)
∴ Δ AOB ≅ Δ BCA
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.

Start Generating Free

Explore more

More "[4 marks sum]" from Congruency: Congruent Triangles→Congruency: Congruent Triangles — all question types→MATHS STD 7 question papers→ICSE Board STD 7 question papers→ICSE Board question paper generator→

Similar questions

Vijay weighed $65 \frac{1}{2} \mathrm{~kg}$. He gained $1 \frac{2}{5} \mathrm{~kg}$ during the first week, $1 \frac{1}{4} \mathrm{~kg}$ during the second week, but lost $\frac{5}{16} \mathrm{~kg}$ during the 16 third week. What was his weight after the third week?
→
A man is thrice as old as his son. After 12 years, he will be twice as old as his son at that time. Find their present ages.
→
Verify: 37 x {8 +(-3)} = 37 x 8 + 37 x – (3)
→
Put the given fraction in ascending order by making denominator equal:
$\frac{5}{6}, \frac{7}{8}, \frac{11}{12} \text { and } \frac{3}{10}$
→
Shyam bought a refrigerator for Rs. 5000 . He paid $\frac{1}{10}$ of the price in cash and the rest in 12 equal monthly instalments. How much had he to pay each month?
→
Evaluate : $\frac{11}{15}-\frac{13}{20}$
→
Ten cards with numbers 1 to 10 written on them are placed in a bag. A card is chosen from the bag at random. Determine the probability of choosing:
(i) 7
(ii) 9 or 10
(iii) a number greater than 4
(iv) a number less than 6
→
Add 13.95 and 1.003; and from the result, subtract the sum of 2.794 and 6.2.
→
Solve: $\frac{4 \mathrm{x}}{3}-\frac{7 \mathrm{x}}{3}=1$
→
A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?
→