## Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

**Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles**

### Congruency: Congruent Triangles Exercise 19 – Selina Concise Mathematics Class 7 ICSE Solutions

**Question 1.**

**State, whether the pairs of triangles given in the following figures are congruent or not:**

**Solution:
**

**Question 2.
**

**In the given figure, prove that:**

**∆ABD ≅ ∆ ACD**

**Solution:**

**Question 3.**

**Prove that:**

**(i) ∆ABC ≡∆ADC**

**(ii) ∠B = ∠D**

**(iii) AC bisects angle DCB**

**Solution:**

**Question 4.**

**Prove that:**

**(i) ∆ABD ≡ ∆ACD**

**(ii) ∠B = ∠C**

**(iii) ∠ADB = ∠ADC**

**(iv) ∠ADB = 90°**

**Solution:**

**Question 5.**

**In the given figure, prove that:**

**(i) ∆ACB ≅ ∆ECD**

**(ii) AB = ED**

**Solution:**

**Question 6.**

**Prove that:**

**(i) ∆ ABC ≅ ∆ ADC**

**(ii) ∠B = ∠D**

**Solution:**

**Question 7.**

**In the given figure, prove that: BD = BC.**

**Solution:**

**Question 8.**

**In the given figure ;**

**∠1 = ∠2 and AB = AC. Prove that:**

**(i) ∠B = ∠C**

**(ii) BD = DC**

**(iii) AD is perpendicular to BC.**

**Solution:**

**Question 9.**

**In the given figure prove tlyat:**

**(i) PQ = RS**

**(ii) PS = QR**

**Solution:**

**Question 10.**

**(i) ∆ XYZ ≅ ∆ XPZ**

**(ii) YZ = PZ**

**(iii) ∠YXZ = ∠PXZ**

**Solution:**

**Question 11.**

**In the given figure, prove that:**

**(i) ∆ABC ≅ ∆ DCB**

**(ii) AC=DB**

**Solution:**

**Question 12.**

**In the given figure, prove that:**

**(i) ∆ AOD ≅ ∆ BOC**

**(ii) AD = BC**

**(iii) ∠ADB = ∠ACB**

**(iv) ∆ADB ≅ ∆BCA**

**Solution:**

**Question 13.**

**ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that:**

**(i) AD = BE**

**(ii)BD = CE**

**Solution:**

**Question 14.**

**Use the informations given in the following figure to prove triangles ABD and CBD are congruent.**

**Also, find the values of x and y.**

**Solution:**

**Question 15.**

**The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:**

**(i) ∆ABD ≅ ∆ACD**

**(ii) AB=AC**

**(iii) ∠B = ∠C**

**Solution:**