Introduction to Congruence

Q. Two objects are said to be congruent if they have same shape and sizes.

1. True
2. False

Q. Two triangles having same side lengths and same corresponding angles are said to be congruent triangles.

1. True
2. False

Q.

Fill in the blank :

Two rectangles are congruent, if they have the same ________ and _________ .

Q. If the red arrow and the blue arrow are congruent, which of the following is/are correct?

1. $x=y$
2. $m\angle a=m\angle b.$
3. $m\angle a=x$

Q. If the squares $ABCD$ and $PQRS$ are congruent. then $a=$.

1. $5$ units
2. $6$ units
3. $7$ units

Q. Three students Varun, Kartik and Sid wrote a statement on a blackboard.
Varun wrote, “Two rectangles are congruent, if they have same perimeter”.
Kartik wrote, “Two squares are congruent, if they have same area”.
Sid wrote, “Two circles are congruent, if they have same diameter”.
Who wrote the correct statement?

1. Varun, Kartik and Sid
2. Kartik and Sid
3. Varun and Kartik
4. Varun and Sid

Q.
If both quadilaterals $ABCD$ and $PQRS$ given in the diagram above have same side length, then $ABCD$ and $PQRS$ are congruent.

1. True
2. False

Q. We have a square with perimeter $52$ cm and an equilateral triangle with perimeter $39$ cm. If two circles have its diameter equal to the side of the square and side of the triangle respectively. Will the circles be congruent?

1. Yes
2. No

Q. Are these two geometrical figures congruent?

1. Yes
2. No

Q. If a triangle $ABC$ is congruent to the triangle $PQR$, it can be represented as:
$△ABC$$△PQR$

1. $\cong$
2. $=$
3. $\equiv$

Q. Why can't a parallelogram and a rhombus, as shown in the figure never be congruent?

1. They have unequal side lengths.
2. They have unequal vertex angles.
3. No, they are congruent.

Q. For the two congruent triangles $ABC$ and $PQR$ as shown in the diagram, choose the correct pair.

1. $a$
2. $b$
3. $x^{\circ }$
4. $y^{\circ }$
5. $5$
6. $8$
7. ${65}^{\circ }$
8. ${55}^{\circ }$

Q. The triangles $ABC$ and $PQR$ are congruent.

1. Yes
2. No

Q. The two triangles DAS and UIP are congruent. Find the value of $\angle ADS$ (in degrees).

Q. Two circles are congruent only if their radii are the same.

1. True
2. False

Q.

If $∆EFG$ and $∆XYZ$ are congruent, then side $EF$$=$__________.

Q. If the two rectangles $ABCD$ and $PSRQ$ are congruent with each other, then $a\times b=$

1. $40$ sq. units
2. $60$ sq. units
3. $80$ sq. units