Maths Triangles Exercise 10.1

Triangles Exercise 10-1

Please Select

Q1 It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR ? Why?

View Solution

Q2 “If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

View Solution

Q3 In the given figure, AB=AC and AP=AQ. Prove that
(i) ∆APC ≅ ∆AQB
(ii) CP = BQ
(iii) ∠APC = ∠AQB.

View Solution

Q4 In the given figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that (i) ∆APC ≅ ∆AQB (ii) CP = BQ (iii) ∠ACP = ∠ABQ.

View Solution

Q5 In the given figure, AD = BC and BD = AC. Prove that :
∠ADB = ∠BCA and ∠DAB = ∠CBA.

View Solution

Q6 In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that
(i) ∆ABD ≅ ∆BAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.

View Solution

Q7 In the given figure, AB = DC and AB || DC. Prove that AD = BC.

View Solution

Q8 In the given figure. AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.

View Solution

Q9 In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that
(i) ∆ACE ≅ ∆DBF
(ii) AE = DF.

View Solution

Q10 In the given figure, AB = AC and D is mid-point of BC. Use SSS rule of congruency to show that
(i) ∆ABD ≅ ∆ACD
(ii) AD is bisector of ∠A
(iii) AD is perpendicular to BC.

View Solution

Q11 Two line segments AB and CD bisect each other at O. Prove that :
(i) AC = BD
(ii) ∠CAB = ∠ABD
(iii) AD || CB
(iv) AD = CB.

View Solution

Q12 In each of the following diagrams, find the values of x and y.

View Solution

Triangles Exercise 10-1

Please Select

Q1 It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR ? Why?

Q2 “If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Q3 In the given figure, AB=AC and AP=AQ. Prove that
(i) ∆APC ≅ ∆AQB
(ii) CP = BQ
(iii) ∠APC = ∠AQB.

Q4 In the given figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that (i) ∆APC ≅ ∆AQB (ii) CP = BQ (iii) ∠ACP = ∠ABQ.

Q5 In the given figure, AD = BC and BD = AC. Prove that :
∠ADB = ∠BCA and ∠DAB = ∠CBA.

Q6 In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that
(i) ∆ABD ≅ ∆BAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.

Q7 In the given figure, AB = DC and AB || DC. Prove that AD = BC.

Q8 In the given figure. AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.

Q9 In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that
(i) ∆ACE ≅ ∆DBF
(ii) AE = DF.

Q10 In the given figure, AB = AC and D is mid-point of BC. Use SSS rule of congruency to show that
(i) ∆ABD ≅ ∆ACD
(ii) AD is bisector of ∠A
(iii) AD is perpendicular to BC.

Q11 Two line segments AB and CD bisect each other at O. Prove that :
(i) AC = BD
(ii) ∠CAB = ∠ABD
(iii) AD || CB
(iv) AD = CB.

Q12 In each of the following diagrams, find the values of x and y.

Contact Us

Get In Touch With Us

Triangles Exercise 10-1

Please Select

Q1 It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR ? Why?

Q2 “If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

Q3 In the given figure, AB=AC and AP=AQ. Prove that (i) ∆APC ≅ ∆AQB (ii) CP = BQ (iii) ∠APC = ∠AQB.

Q4 In the given figure, AB = AC, P and Q are points on BA and CA respectively such that AP = AQ. Prove that (i) ∆APC ≅ ∆AQB (ii) CP = BQ (iii) ∠ACP = ∠ABQ.

Q5 In the given figure, AD = BC and BD = AC. Prove that : ∠ADB = ∠BCA and ∠DAB = ∠CBA.

Q6 In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that (i) ∆ABD ≅ ∆BAC (ii) BD = AC (iii) ∠ABD = ∠BAC.

Q7 In the given figure, AB = DC and AB || DC. Prove that AD = BC.

Q8 In the given figure. AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.

Q9 In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that (i) ∆ACE ≅ ∆DBF (ii) AE = DF.

Q10 In the given figure, AB = AC and D is mid-point of BC. Use SSS rule of congruency to show that (i) ∆ABD ≅ ∆ACD (ii) AD is bisector of ∠A (iii) AD is perpendicular to BC.

Q11 Two line segments AB and CD bisect each other at O. Prove that : (i) AC = BD (ii) ∠CAB = ∠ABD (iii) AD || CB (iv) AD = CB.

Q12 In each of the following diagrams, find the values of x and y.

Contact Us

Get In Touch With Us

Q3 In the given figure, AB=AC and AP=AQ. Prove that
(i) ∆APC ≅ ∆AQB
(ii) CP = BQ
(iii) ∠APC = ∠AQB.

Q5 In the given figure, AD = BC and BD = AC. Prove that :
∠ADB = ∠BCA and ∠DAB = ∠CBA.

Q6 In the given figure, ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that
(i) ∆ABD ≅ ∆BAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.

Q9 In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that
(i) ∆ACE ≅ ∆DBF
(ii) AE = DF.

Q10 In the given figure, AB = AC and D is mid-point of BC. Use SSS rule of congruency to show that
(i) ∆ABD ≅ ∆ACD
(ii) AD is bisector of ∠A
(iii) AD is perpendicular to BC.

Q11 Two line segments AB and CD bisect each other at O. Prove that :
(i) AC = BD
(ii) ∠CAB = ∠ABD
(iii) AD || CB
(iv) AD = CB.