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Triangle congruence worksheet






Given below are the Class 9 Maths Triangle congruence worksheet
(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
  1. $AB =PQ \; , \; BC=QR \; and \; AC=PR$
  2. $BC=QR \; , \; \angle B= \angle Q \; , \;\angle C=\angle R$
  3. $AB=PQ, BC=QR, \angle C= \angle P$
  4. $AB=PQ, BC=QR, \angle B= \angle Q$
  5. $AB=PQ \; , \; \angle A= \angle P \;,\; \angle C= \angle R$
  6. $AB =PQ \; , \; BC=QR$
  7. $ \angle B= \angle Q \; , \; \angle C= \angle R$
  8. $ \angle A= \angle P, \angle B=\angle Q ,\angle C= \angle R$
  9. $AB=PR , \angle A= \angle P, \angle B=\angle R$




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


Multiple choice Questions

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


Question 5
In triangle ABC , AB=AC and D is the point inside triangle such that BD=DC as shown in figure
triangle congruence worksheet
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

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

Question 7
AD is the median of the triangle . Which of the following is true?
Triangle question
a. $AB+BC+AC > 2AD$
b. $AB +BC > AC$
c. $AB+BC+AC> AD$
d. none of these

Question 8
triangle congruence worksheet
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

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


Question 10
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. $20^0,60^0$


Question 11
triangle congruence worksheet
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


Match the column

Column AColumn B
Point of intersection of altitude Circumcenter
Point of intersection of Median In-centre
Point of intersection of angle bisector Orthocenter
Point of intersection of perpendicular bisector of sides Centroid

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Reference Books for class 9 Math

Given below are the links of some of the reference books for class 9 Math.

  1. Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
  2. Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
  3. Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
  4. Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.



Class 9 Maths Class 9 Science





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