# Triangle congruence worksheet

Given below are the Class 9 Maths Triangle congruence worksheet
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice 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

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?

a. $AB+BC+AC > 2AD$
b. $AB +BC > AC$
c. $AB+BC+AC> AD$
d. none of these

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

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

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 A Column 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