NCERT Solutions Class 9 Mathematics Chapter 7 Triangles Download In Pdf

Chapter 7 Triangles Download in Pdf

EXERCISE 7.1

**Question 1.** In quadrilateral ACBD,
AC = AD and AB bisects âˆ A
(see Fig. 7.16). Show that Î” ABC Î” ABD.
What can you say about BC and BD?

**
Question 2 **. ABCD is a quadrilateral in which AD = BC and
âˆ DAB = âˆ CBA (see Fig. 7.17). Prove that

(i) Î” ABD Î” BAC

(ii) BD = AC

(iii) âˆ ABD = âˆ BAC.

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

**Question 4**. l and m are two parallel lines intersected by
another pair of parallel lines p and q
(see Fig. 7.19). Show that Î” ABC Î” CDA.

**Question 5**. line l is the bisector of an angle âˆ A and B is any
point on l. BP and BQ are perpendiculars from B
to the arms of âˆ A (see Fig. 7.20). Show that:

(i) Î” APB Î” AQB

(ii) BP = BQ or B is equidistant from the arms
of âˆ A.

**Question 6**. In Fig. 7.21, AC = AE, AB = AD and
âˆ BAD = âˆ EAC. Show that BC = DE.

**
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
âˆ BAD = âˆ ABE and âˆ EPA = âˆ DPB
(see Fig. 7.22). Show that

(i) Î” DAP Î” EBP

(ii) AD = BE

**Question 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) Î” AMC Î” BMD

(ii) âˆ DBC is a right angle.

(iii) Î” DBC Î” ACB

(iv) CM =
1
2 AB

EXERCISE 7.2

**Question 1**. In an isosceles triangle ABC, with AB = AC, the bisectors of âˆ B and âˆ C intersect
each other at O. Join A to O. Show that :

(i) OB = OC

(ii) AO bisects âˆ A

**
Question 2**. In Î” ABC, AD is the perpendicular bisector of BC
(see Fig. 7.30). Show that Î” ABC is an isosceles
triangle in which AB = AC.

**
Question 3**. ABC is an isosceles triangle in which altitudes
BE and CF are drawn to equal sides AC and AB
respectively (see Fig. 7.31). Show that these
altitudes are equal.

**Question 4**. ABC is a triangle in which altitudes BE and CF to
sides AC and AB are equal (see Fig. 7.32). Show
that

(i) Î” ABE Î” ACF

(ii) AB = AC, i.e., ABC is an isosceles triangle.

**
Question 5**. ABC and DBC are two isosceles triangles on the
same base BC (see Fig. 7.33). Show that
âˆ ABD = âˆ ACD.

**
Question 6**. Î”ABC is an isosceles triangle in which AB = AC.
Side BA is produced to D such that AD = AB
(see Fig. 7.34). Show that âˆ BCD is a right angle.
7. ABC is a right angled triangle in which âˆ A = 90Â°
and AB = AC. Find âˆ B and âˆ C.

**Question 7**. Show that the angles of an equilateral triangle
are 60Â° each.

EXERCISE 7.3

**Question 1**. Î” ABC and Î” DBC are two isosceles triangles on
the same base BC and vertices A and D are on the
same side of BC (see Fig. 7.39). If AD is extended
to intersect BC at P, show that

(i) Î” ABD Î” ACD

(ii) Î” ABP Î” ACP

(iii) AP bisects âˆ A as well as âˆ D.

(iv) AP is the perpendicular bisector of BC.

**
Question 2**. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that

(i) AD bisects BC

(ii) AD bisects âˆ A.

**
Question 3**. Two sides AB and BC and median AM
of one triangle ABC are respectively
equal to sides PQ and QR and median
PN of Î” PQR (see Fig. 7.40). Show that:

(i) Î” ABM Î” PQN

(ii) Î” ABC Î” PQR

**
Question **4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence
rule, prove that the triangle ABC is isosceles.

**
Question 5**. ABC is an isosceles triangle with AB = AC. Draw AP âŠ¥ BC to show that
âˆ B = âˆ C.

EXERCISE 7.4

**
Question 1**. Show that in a right angled triangle, the
hypotenuse is the longest side.

**
Question 2**. In Fig. 7.48, sides AB and AC of Î” ABC are
extended to points P and Q respectively. Also,
âˆ PBC < âˆ QCB. Show that AC > AB.
3. In Fig. 7.49, âˆ B < âˆ A and âˆ C < âˆ D. Show that
AD < BC.

**
Question 3**. AB and CD are respectively the smallest and
longest sides of a quadrilateral ABCD
(see Fig. 7.50). Show that âˆ A > âˆ C and
âˆ B > âˆ D.

**
Question 4**. In Fig 7.51, PR > PQ and PS bisects âˆ QPR. Prove
that âˆ PSR > âˆ PSQ.

EXERCISE 7.5

**Question 1** . ABC is a triangle. Locate a point in the interior of Î” ABC which is equidistant from all
the vertices of Î” ABC.

**Question 2**. In a triangle locate a point in its interior which is equidistant from all the sides of the
triangle.

**Question 3**. In a huge park, people are concentrated at three
points (see Fig. 7.52):

A : where there are different slides and swings
for children,

B : near which a man-made lake is situated,

C : which is near to a large parking and exit.
Where should an icecream parlour be set up so
that maximum number of persons can approach
it?
(Hint : The parlour should be equidistant from A, B and C)

**Question 4**. Complete the hexagonal and star shaped Rangolies [see Fig. 7.53(i) and (ii)] by filling
them with as many equilateral triangles of side 1 cm as you can. Count the number of
triangles in each case. Which has more triangles?

Please send your queries to ncerthelp@gmail.com you can aslo visit our facebook page to get quick help. Link of our facebook page is given in sidebar

- Chapter 3 Coordinate Geometry
- Chapter 4 Linear Equations In Two Variables
- Chapter 7 Triangles
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Heronâ€™s Formula
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

- NCERT Solutions for Class 9 Science Maths Hindi English Math
- NCERT Solutions for Class 10 Maths Science English Hindi SST
- Class 11 Maths Ncert Solutions Biology Chemistry English Physics
- Class 12 Maths Ncert Solutions Chemistry Biology Physics pdf

- Class 1 Model Test Papers Download in pdf
- Class 5 Model Test Papers Download in pdf
- Class 6 Model Test Papers Download in pdf
- Class 7 Model Test Papers Download in pdf
- Class 8 Model Test Papers Download in pdf
- Class 9 Model Test Papers Download in pdf
- Class 10 Model Test Papers Download in pdf
- Class 11 Model Test Papers Download in pdf
- Class 12 Model Test Papers Download in pdf

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.