Congruent triangles class 9 worksheet with answers
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
Subjective Questions
Question 1
Let ABC and PQR are two triangles.
Which cases the triangles will be congruent? Write down the congruence equation
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
Question 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 $ABC \cong PQR$ 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
Question 4
In a triangle ABC , $\angle A=60^0$ ,#\angle B=40^0$, which side is the longest
a. AB
b. BC
c. AC Solutions
(a)
As $\angle C=80^0$ is the highest angle
Question 5
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 Solutions
In triangle ABD and ACD
AD=AC
BD=DC
AD is common
So $\Delta ABD \cong \Delta ACD$
So all the above are true
Question 6
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 Solutions
(a)
Sum of the opposite two interior angle =Exterior angle
$50+x=110$ => $x=60$
Now $60+50+z=180$
$z=70$
Question 7
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 Solutions
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
$AB+BC > AC$
Question 8
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 Solutions
(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
$AB=CD$
$OA=OD$
Question 9
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)
$P=90^0$
Since PQ=PR
$ \angle Q=\angle R$
So $Q=R=45^0$
Question 11
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 $\angle C=\angle D$
Match the column
Question 12
Short answer type questions
Question 13
PQ > PR and QS and RS are the bisectors of angle Q and R, respectively. Show that SQ > SR. Solutions
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)
Question 14
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 Solutions
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
Question 15
S is any point in the interior of triangle PQR. Show that SQ + SR < PQ + PR Solutions
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
Summary
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 Download this assignment as pdf
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