Page 1 Cbse-spot.blogspot.com 1 Class IX Chapter 7 – Triangles Maths Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ?ABC ?ABD. What can you say about BC and BD? Answer: In ?ABC and ?ABD, AC = AD (Given) CAB = DAB (AB bisects A) AB = AB (Common) ?ABC ?ABD (By SAS congruence rule) BC = BD (By CPCT) Therefore, BC and BD are of equal lengths. Question 2: ABCD is a quadrilateral in which AD = BC and DAB = CBA (See the given figure). Page 2 Cbse-spot.blogspot.com 1 Class IX Chapter 7 – Triangles Maths Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ?ABC ?ABD. What can you say about BC and BD? Answer: In ?ABC and ?ABD, AC = AD (Given) CAB = DAB (AB bisects A) AB = AB (Common) ?ABC ?ABD (By SAS congruence rule) BC = BD (By CPCT) Therefore, BC and BD are of equal lengths. Question 2: ABCD is a quadrilateral in which AD = BC and DAB = CBA (See the given figure). Cbse-spot.blogspot.com 2 Prove that (i) ?ABD ?BAC (ii) BD = AC (iii) ABD = BAC. Answer: In ?ABD and ?BAC, AD = BC (Given) DAB = CBA (Given) AB = BA (Common) ?ABD ?BAC (By SAS congruence rule) BD = AC (By CPCT) And, ABD = BAC (By CPCT) Question 3: AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB. Page 3 Cbse-spot.blogspot.com 1 Class IX Chapter 7 – Triangles Maths Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ?ABC ?ABD. What can you say about BC and BD? Answer: In ?ABC and ?ABD, AC = AD (Given) CAB = DAB (AB bisects A) AB = AB (Common) ?ABC ?ABD (By SAS congruence rule) BC = BD (By CPCT) Therefore, BC and BD are of equal lengths. Question 2: ABCD is a quadrilateral in which AD = BC and DAB = CBA (See the given figure). Cbse-spot.blogspot.com 2 Prove that (i) ?ABD ?BAC (ii) BD = AC (iii) ABD = BAC. Answer: In ?ABD and ?BAC, AD = BC (Given) DAB = CBA (Given) AB = BA (Common) ?ABD ?BAC (By SAS congruence rule) BD = AC (By CPCT) And, ABD = BAC (By CPCT) Question 3: AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB. Cbse-spot.blogspot.com 3 Answer: In ?BOC and ?AOD, BOC = AOD (Vertically opposite angles) CBO = DAO (Each 90º) BC = AD (Given) ?BOC ?AOD (AAS congruence rule) BO = AO (By CPCT) CD bisects AB. Question 4: l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ?ABC ?CDA. Answer: In ?ABC and ?CDA, Page 4 Cbse-spot.blogspot.com 1 Class IX Chapter 7 – Triangles Maths Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ?ABC ?ABD. What can you say about BC and BD? Answer: In ?ABC and ?ABD, AC = AD (Given) CAB = DAB (AB bisects A) AB = AB (Common) ?ABC ?ABD (By SAS congruence rule) BC = BD (By CPCT) Therefore, BC and BD are of equal lengths. Question 2: ABCD is a quadrilateral in which AD = BC and DAB = CBA (See the given figure). Cbse-spot.blogspot.com 2 Prove that (i) ?ABD ?BAC (ii) BD = AC (iii) ABD = BAC. Answer: In ?ABD and ?BAC, AD = BC (Given) DAB = CBA (Given) AB = BA (Common) ?ABD ?BAC (By SAS congruence rule) BD = AC (By CPCT) And, ABD = BAC (By CPCT) Question 3: AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB. Cbse-spot.blogspot.com 3 Answer: In ?BOC and ?AOD, BOC = AOD (Vertically opposite angles) CBO = DAO (Each 90º) BC = AD (Given) ?BOC ?AOD (AAS congruence rule) BO = AO (By CPCT) CD bisects AB. Question 4: l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ?ABC ?CDA. Answer: In ?ABC and ?CDA, Cbse-spot.blogspot.com 4 BAC = DCA (Alternate interior angles, as p || q) AC = CA (Common) BCA = DAC (Alternate interior angles, as l || m) ?ABC ?CDA (By ASA congruence rule) Question 5: Line l A is the bisector of an angle and B is any point on l. BP and BQ are perpendiculars from B to the arms of A (see the given figure). Show that: i) ?APB ?AQB ( ii) BP = BQ or B is equidistant from the arms of ( A. Answer: In ?APB and ?AQB, APB = AQB (Each 90º) PAB = QAB (l is the angle bisector of A) AB = AB (Common) ?APB ?AQB (By AAS congruence rule) BP = BQ (By CPCT) rms of A. Or, it can be said that B is equidistant from the a Question 6: In the given figure, AC = AE, AB = AD and BAD = EAC. Show that BC = DE. Page 5 Cbse-spot.blogspot.com 1 Class IX Chapter 7 – Triangles Maths Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ?ABC ?ABD. What can you say about BC and BD? Answer: In ?ABC and ?ABD, AC = AD (Given) CAB = DAB (AB bisects A) AB = AB (Common) ?ABC ?ABD (By SAS congruence rule) BC = BD (By CPCT) Therefore, BC and BD are of equal lengths. Question 2: ABCD is a quadrilateral in which AD = BC and DAB = CBA (See the given figure). Cbse-spot.blogspot.com 2 Prove that (i) ?ABD ?BAC (ii) BD = AC (iii) ABD = BAC. Answer: In ?ABD and ?BAC, AD = BC (Given) DAB = CBA (Given) AB = BA (Common) ?ABD ?BAC (By SAS congruence rule) BD = AC (By CPCT) And, ABD = BAC (By CPCT) Question 3: AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB. Cbse-spot.blogspot.com 3 Answer: In ?BOC and ?AOD, BOC = AOD (Vertically opposite angles) CBO = DAO (Each 90º) BC = AD (Given) ?BOC ?AOD (AAS congruence rule) BO = AO (By CPCT) CD bisects AB. Question 4: l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ?ABC ?CDA. Answer: In ?ABC and ?CDA, Cbse-spot.blogspot.com 4 BAC = DCA (Alternate interior angles, as p || q) AC = CA (Common) BCA = DAC (Alternate interior angles, as l || m) ?ABC ?CDA (By ASA congruence rule) Question 5: Line l A is the bisector of an angle and B is any point on l. BP and BQ are perpendiculars from B to the arms of A (see the given figure). Show that: i) ?APB ?AQB ( ii) BP = BQ or B is equidistant from the arms of ( A. Answer: In ?APB and ?AQB, APB = AQB (Each 90º) PAB = QAB (l is the angle bisector of A) AB = AB (Common) ?APB ?AQB (By AAS congruence rule) BP = BQ (By CPCT) rms of A. Or, it can be said that B is equidistant from the a Question 6: In the given figure, AC = AE, AB = AD and BAD = EAC. Show that BC = DE. Cbse-spot.blogspot.com 5 Answer: It is given that BAD = EAC BAD + DAC = EAC + DAC BAC = DAE In ?BAC and ?DAE, AB = AD (Given) BAC = DAE (Proved above) AC = AE (Given) ?BAC ?DAE (By SAS congruence rule) BC = DE (By CPCT) Question 7: AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that BAD = ABE and EPA = DPB (See the given figure). Show that i) ?DAP ?EBP ( (ii) AD = BERead More

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