NCERT Class 9 Mathematics Triangles Formative Assignments Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2023)

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Subjective Questions

1. Let ABC and PQR are two triangles.

Which cases the triangles will be congruent? Write down the congruence equation

a)

b)

c)

d)

e)

f)

g)

h)

i)

Solution

a) The three sides are equal to corresponding three sides. From SSS congruence, ABC is congruent to PQR

b) Two angles and included side are equal, so from ASA congruence, ABC is congruent to PQR

c) Two sides are equal but the angle is not the included, So ABC is not congruent to POR

d) Two sides are equal and included angle is equal so from SAS congruence, ABC is congruent to PQR

e) Two angles and included side are equal, so from ASA congruence, ABC is congruent to POR

f) Just two sides are equal; So ABC is not congruent to PQR

g) Just two angles are equal, there is no information about side, and So ABC is not congruent to PQR

h) All the angles are equal. This does not satisfy any congruence theorem, So ABC is not congruent to PQR

j) Two sides are equal and included angle is equal so from SAS congruence, ABC is congruent to PRQ

True or False statement

2) True or False statement

a) We cannot construct a triangle of side 9,5, 4 cm

b) In a Right angle triangle, hyponotuse is the longest side

c) Centroid is the point of intersection of the median of the triangles

d) A triangle can have two obtuse angles

e) Orthocenter is the point of intersection of altitudes

f) If then

g) If a triangle ABC such that , Then

h) Midpoint of the hypotenuse of right angled triangle is circumcenter

Solution

a) True

b) True

c) True

d) False

e) True

f) False

g) True

h) True

Multiple choice Questions

4) In a triangle , which side is the longest?

a) AB

b) BC

c) AC

Solution (a)

As is the highest angle

5. In triangle ABC, and D is the point inside triangle such that as shown in figure

Which of the following is true?

a)

b)

c)

d) All the above

Solution

In triangle ABD and ACD

AD is common

So

So all the above are true

6) An exterior angle of the triangle is , one of the opposite interior angle is 50°.

What are the other two angles?

a)

b)

c)

d) None of the above

Solution (a)

Sum of the opposite two interior angle = Exterior angle

Now

7) AD is the median of the triangle. Which of the following is true?

1.

2.

3.

4. None of these

Solution: 1 and 2

In triangle ADB

In triangle ADO

Adding both

Now

So

Also in triangle ABC

8)

In the above Tigure O is the midpoint BC. Which of the following is true?

a)

b) O is the midpoint of AD

c)

d) All the above

Solution (d)

In and

OB and OC

So from AAS congruence, we have

Now from CPCT, we have

9) In an isosceles triangle AABC with . D is midpoint on BC.

Which of the following is true?

a) Orthocenter lies on line AD

b) AD is the perpendicular bisector BC

c) Centroid lies on the line AD

d) AD is the bisector of angle A

Solution: (a) (b) (c) (d)

10) PQR is a right angle triangle in with and PQ = PR. What is the value of Q and R?

a)

b)

c)

Solution (a)

Since

So

In the above quadrilateral ACBD, we have and AB bisect the

Which of the following is true?

a)

b)

c)

d) None of the above

Solution (a) , (b) , (c)

In triangle ABC and ABD, we have

By SAS, we have

Now we have and

Match the column