Given below are the **Class 9 Maths** Triangle congruence worksheet with answers

(a) Concepts questions

(b) Calculation problems

(c) Multiple choice questions

(d) Long answer questions

(e) Fill in the blanks

(f)Subjective Questions

(a) Concepts questions

(b) Calculation problems

(c) Multiple choice questions

(d) Long answer questions

(e) Fill in the blanks

(f)Subjective Questions

Let ABC and PQR are two triangles.

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

- $AB =PQ \; , \; BC=QR \; and \; AC=PR$
- $BC=QR \; , \; \angle B= \angle Q \; , \;\angle C=\angle R$
- $AB=PQ, BC=QR, \angle C= \angle P$
- $AB=PQ, BC=QR, \angle B= \angle Q$
- $AB=PQ \; , \; \angle A= \angle P \;,\; \angle C= \angle R$
- $AB =PQ \; , \; BC=QR$
- $ \angle B= \angle Q \; , \; \angle C= \angle R$
- $ \angle A= \angle P, \angle B=\angle Q ,\angle C= \angle R$
- $AB=PR , \angle A= \angle P, \angle B=\angle R$

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

$ \Delta ABC \cong \Delta PQR$ - Two angles and included side are equal ,so from ASA congruence, ABC is congruent to PQR

$ \Delta ABC \cong \Delta PQR$ - Two sides are equal but the angle is not the included ,So ABC is not congruent to PQR

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

$ \Delta ABC \cong \Delta PQR$ - Two angles and other side are equal ,so from AAS congruence, ABC is congruent to PQR

$ \Delta ABC \cong \Delta PQR$ - Just two sides are equal, So ABC is not congruent to PQR

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

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

- Two sides are equal and included angle is equal So from SAS congruence, ABC is congruent to PRQ

$ \Delta ABC \cong \Delta PQR$

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 $ABC \cong PQR$ then AC=PQ

g. if a triangle ABC such that AB > BC , Then $\angle C > \angle A$

h. Mid point of the hypotenuse of right angled triangle is circumcenter

a.True

b.True

c.True

d.False

e.True

f.False

g.True

h.True

In a triangle ABC , $\angle A=60^0$ ,#\angle B=40^0$, which side is the longest

a. AB

b. BC

c. AC

(a)

As $\angle C=80^0$ is the highest angle

In triangle ABC , AB=AC and D is the point inside triangle such that BD=DC as shown in figure

Which of the following is true

a. $\Delta ABD \cong \Delta ACD$

b. $\angle ABD= \angle ACD$

c. $\angle DAC= \angle DAB$

d. All the above

In triangle ABD and ACD

AD=AC

BD=DC

AD is common

So $\Delta ABD \cong \Delta ACD$

So all the above are true

An exterior angle of the triangle is $110^0$ , One of the opposite interior angle is $50^0$

What are the other two angles

a. $60^0,70^0$

b. $55^0,55^0$

c. $70^0,50^0$

d. None of the above

(a)

Sum of the opposite two interior angle =Exterior angle

$50+x=110$ => $x=60$

Now $60+50+z=180$

$z=70$

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

a. $AB+BC+AC > 2AD$

b. $AB +BC > AC$

c. $AB+BC+AC> AD$

d. none of these

Answer a and b

In triangle ADB

$AB +BD > AD$

In triangle ADC

$AC+DC > AD$

Adding both

$AB+AC +BD+DC> 2AD$

Now $BD+DC=BC$

So

$AB +AC+BC > 2AD$

Also in triangle ABC

$AB+BC > AC$

In the above figure AB || CD ,O is the mid point BC. Which of the following is true

a. $ \Delta AOB \cong \Delta DOC$

b. O is the mid point of AD

c. $AB=CD$

d. All the above

(d)

In $ \Delta AOB \; and \; \Delta DOC$

$\angle OAB= \angle ODC$

$\angle OBA=\angle OCD$

OB and OC

So from AAS congruence ,we have

$ \Delta AOB \cong \Delta DOC$

Now from CPCT ,we have

$AB=CD$

$OA=OD$

In an isosceles triangle ΔABC with AB = AC. D is mid point 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

(a) (b) (c) (d)

PQR is a right angle triangle in with $P=90^0$ and PQ=PR . What is the value of Q and R

a. $45^0,45^0$

b. $30^0,60^0$

c. $20^0,60^0$

(a)
$P=90^0$

Since PQ=PR

$ \angle Q=\angle R$

So $Q=R=45^0$

In the above quadrilateral ACBD, we have AC=AD and AB bisect the ∠A

Which of the following is true

a. $ \Delta ABC \cong \Delta ABD$

b. BC=BD

c. $ \angle C= \angle D$

d. None of the above

(a) ,(b) ,(c)

In triangle ABC and ABD ,we have

AC=AD

$\angle CAB=\angle BAD$

AB=AB

By SAS ,we have

$ \Delta ABC \cong \Delta ABD$

Now we have BC=BD and $\angle C=\angle D$

PQ > PR and QS and RS are the bisectors of angle Q and R, respectively. Show that SQ > SR.

PQ > PR (Given)

Therefore, ∠ R > ∠ Q(Angles opposite the longer side is greater)

So, ∠ SRQ > ∠ SQR(Half of each angle)

Therefore, SQ > SR(Side opposite the greater angle will be longer)

l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively

l || m (Given)

Therefore, ∠ ACM = ∠ BDM (Alternate interior angles)

and ∠ CAM = ∠ DBM (Alternate interior angles)

Also, AM = MB (Given)

So, $\Delta AMC \cong \Delta BMD$ (ASA)

Therefore,CM=MD i.e mid point

S is any point in the interior of triangle PQR. Show that SQ + SR < PQ + PR

Produce QS to intersect PR at T

From Triangle PQT, we have

PQ + PT > QT(Sum of any two sides is greater than the third side)

i.e., PQ + PT > SQ + ST--- (1)

From Triang;e TSR, we have

ST + TR > SR-- (2)

Adding (1) and (2), we get

PQ + PT + ST + TR > SQ + ST + SR

i.e., PQ + PT + TR > SQ + SR

i.e., PQ + PR > SQ + SR

or SQ + SR < PQ + PR

This Congruent triangles class 9 worksheet with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail. You can download this test as pdf also as below

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