Congruence of Triangles

Q.

Find the perimeter of an equilateral triangle whose each side measures $12cm$.

Q. It is given that $\Delta ABC\cong \Delta FDE$ and AB = 5 cm, $\angle B={40}^{\circ }\text{and}\angle A={80}^{\circ }$, then which of the following is true?

1. DF = 5 cm and $\angle F={60}^{\circ }$
2. DF = 5 cm and $\angle E={60}^{\circ }$
3. DE = 5 cm and $\angle D={60}^{\circ }$
4. DE = 5 cm and $\angle E={60}^{\circ }$​​​​​​

Q. The congruent sides of an isosceles triangle are 4 cm each. If the perimeter is 14 cm, then the 3rd side is .

1. 6 cm
2. 8 cm
3. 10 cm

Q.

The following triangle ABC is rotated through ${90}^{\circ }$ in anti-clockwise direction and then reflected through a vertical mirror. Then the mirror image hence obtained is not congruent to the initially taken triangle ABC.

1. True

2. False

Q.

In the given figure, if $\angle BCA=\angle RPQ={15}^{\circ },$
then $\angle PQR$ is ______.

1. ${45}^{\circ }$

2. ${35}^{\circ }$

3. ${15}^{\circ }$

4. ${55}^{\circ }$

Q.

In the following figure find the value of $x$.

Q. In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of $\angle BCD$?

Q. $△ABC$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. $\angle BCD$ is equal to

1. ${90}^{\circ }$
2. ${45}^{\circ }$
3. ${37}^{\circ }$

Q.

In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. The measure of $\angle DAC$ is

1. ${50}^{\circ }$
2. ${150}^{\circ }$
3. ${130}^{\circ }$
4. ${80}^{\circ }$

Q. ABC is an isosceles triangle in which
AB = AC. Side BA is produced to D such that AD = AB. What is $\angle$ BCD in terms of degrees?

1. 90

Q.

$△ABC$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of $\angle BCD$?

Q.

In the given figure, D and E are mid points of sides AB and AC of $△$ABC. Which of the following is true?

1. DE = ​ BC, by converse of mid point theorem

2. DE = AB, by mid point theorem

3. DE = AB, by converse of mid point theorem

4. DE = BC, by mid point theorem

Q. Any two triangles are said to be congruent if

1. any one corresponding angle is equal.
2. any one corresponding side is equal.
3. all their corresponding sides are equal.
4. any two corresponding angles are equal.

Q.

For what value of $x$ will $△ABC\cong △XYZ$ ?

1. $x={80}^{\circ }$

2. $x={70}^{\circ }$

3. $x={50}^{\circ }$

4. $x={30}^{\circ }$

Q.

The perimeter of a triangle in which all the angles are congruent and one of the side lengths is equal to 4 cm is:

1. 12 cm

2. 10 cm

3. 9 cm

4. 8 cm

Q. In $\Delta$ ABC, $\angle A=\angle C$ and AB = 6 units. What is the length of BC?

1. 6

Q. The circumference of a $\Delta ABC$ is O. prove that $\angle OBC+\angle BAC={90}^{\circ }$.

Q.

The congruent sides of an isosceles triangle are 4 cm each. If the perimeter is 14 cm, then the 3rd side is:

1. 6 cm

2. 11 cm

3. 8 cm

4. 3 cm

Q.

The congruent sides of an isosceles triangle are 4 cm each. If the perimeter is 14 cm, then the 3rd side is:

1. 6 cm

2. 11 cm

3. 8 cm

4. 3 cm

Q. If $△ABC\cong △DEF$, then

1. AB = DE
2. BC = EF
3. CA = FD
4. AB = EF
5. BC = DE
6. $\angle$B = $\angle$F
7. $\angle$C = $\angle$F
8. $\angle$A = $\angle$D

Q.

If triangle PQR is congruent to triangle XYZ, then which of the following is true?

1. angle P is congruent to angle Y

2. angle Q is congruent to angle Z

3. angle R is congruent to angle X

4. angle R is congruent to angle Z

Q.

If a triangle ABC is congruent to triangle DEF, then

1. side BC is congruent to side DE

2. side AB is congruent to side DE

3. side AB is congruent to side FD

4. side CA is congruent to side DE

Q.

$△$ABC is an isosceles triangle, in which AB=AC. Side BA is produced to D such that AD=AB. $\angle$BCD is equal to ___.

1. ${90}^{\circ }$

2. ${45}^{\circ }$

3. ${37}^{\circ }$

4. Cannot be determined

Q. In $\Delta ABC$ and $\Delta DBC,AC=BD$ and $\angle ABC=\angle BCD={90}^o$. Then $\Delta ABC\cong \Delta DCB$ by the postulate

1. SSS
2. RHS
3. SAS
4. ASA

Q.

$△ABC$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. $\angle BCD$ is equal to ____.

1. ${90}^{\circ }$

2. ${45}^{\circ }$

3. ${37}^{\circ }$

4. Cannot be determined

Q. In a quadrilateral $ABCD,AB=AD$ and $CB=CD$. Then prove that $AC$ is perpendicular bisector of $BD$.

Q.

In the following figure if XY is the mirror, then $△ABC$ congruent to $△A{B}^{\prime }{C}^{\prime }$.

1. True

2. False

Q.

If triangle ABC is congruent to triangle PQR, then

1. side AB is congruent to side QR

2. angle P is congruent to angle B

3. side PQ is congruent to side BC

4. angle B is congruent to angle Q

Q.

Refer to the following figure:
D and C are equidistant from O.
If any point P is located such that $△ODP$ is congurent to $△OCP$, then P lies on the ________.

1. angular bisector of $\angle ODP$
2. altitude of $△DOC$ to side DC
3. angle bisector of $\angle DOC$
4. None of the above