## 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:**