NCERT Solutions Class 9 Maths Chapter 7 – Triangles Exercise 7.1

Chapter 7 – Triangles Exercise 7.1

(Q 1) In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig. 7.16). Show that ∆ABC≅ ∆ABD. What can you say about BC and BD?

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(Q 2) ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that:- (i)∆ABD≅ ∆BAC (ii)BD=AC (iii) ∠ ABD = ∠ BAC

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(Q 3) AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

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(Q 4) l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ∆ABC ≅ ∆CDA.

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(Q 5) Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A (see Fig. 7.20). Show that:
(i)∆APB ≅∆AQB
(ii)BP=BQ or B is equdistant from the arms of ∠ A

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(Q 6) In Fig. 7.21, AC = AE, AB = AD and ∠ BAD = ∠EAC. Show that BC = DE.

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(Q 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 Fig. 7.22). Show that ∆DAP ≅ ∆EBP AD=BE

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(Q 8) In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B
(see Fig. 7.23). Show that:
(i) ∆AMC≅ ∆BMD
(ii) ∠DBC is a right angle
(iii) ∆DBC≅ ∆ACB
(iv) CM=1/2AB

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