Selina solutions concise mathematica class 7 icse Solutions for Chapter 19 congruency congruent triangles

Q1) State, whether the pairs of triangles given in the following figures are congruent or not:

Q2) In the given figure, prove that: ∆ABD ≅ ∆ ACD

Q3) Prove that:

(i) ∆ABC ≡∆ADC (ii) ∠B = ∠D (iii) AC bisects angle DCB

Q4) Prove that:

(i) ∆ABD ≡ ∆ACD (ii) ∠B = ∠C

(iii) ∠ADB = ∠ADC (iv) ∠ADB = 90°

Q5) In the given figure, prove that:

(i) ∆ACB ≅ ∆ECD (ii) AB = ED

Q6) Prove that: (i) ∆ ABC ≅ ∆ ADC (ii) ∠B = ∠D

Q7) In the given figure, prove that: BD = BC.

Q8) In the given figure ; ∠1 = ∠2 and AB = AC. Prove that:

(i) ∠B = ∠C

(ii) BD = DC

(iii) AD is perpendicular to BC.

Q9) In the given figure prove tlyat: (i) PQ = RS (ii) PS = QR

Q10) (i) ∆ XYZ ≅ ∆ XPZ

(ii) YZ = PZ

(iii) ∠YXZ = ∠PXZ

Q11) In the given figure, prove that:

(i) ∆ABC ≅ ∆ DCB (ii) AC=DB

Q12) In the given figure, prove that:

(i) ∆ AOD ≅ ∆ BOC

(ii) AD = BC

(iii) ∠ADB = ∠ACB

(iv) ∆ADB ≅ ∆BCA

Q13) ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that:

(i) AD = BE

(ii) BD = CE

Q14) Use the information given in the following figure to prove triangles ABD and CBD are congruent. Also, find the values of x and y.

Q15) 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