Corresponding Parts of Congruent Triangles

Q.

Question 2 (b)
You want to show that $\Delta ART\cong \Delta PEN$
If it is given that $\angle T=\angle N$ and you are to use SAS criterion, you need to have:
i) RT = and ii) PN =

Q.

Question 1 (b)
Which congruence criterion do you use in the following?
Given: RP = ZX, RQ = ZY, $\Delta PRQ=\Delta XZY$
So $\Delta PQR=\Delta XY$

Q.

The perimeter of $△$ABC is 18cm. If AB = 5 cm and QR = 7cm, then the length of PQ (in cm) is ___.

Q.

In the given figure, if $\angle$ACB = ${30}^{\circ }$. The value of $\angle$ACD is ___${}^{\circ }$.

Q.

The ratio of the corresponding sides of two similar triangles is 1 : 3. The ratio of their corresponding heights is _________.

1. 1:3

2. 3:1

3. 1:9

4. 9:1

Q.

In the given figure, if $\angle$ACB = ${30}^{\circ }$, the value of $\angle$ACD is .........

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

2. ${60}^{\circ }$

3. ${30}^{\circ }$

4. ${75}^{\circ }$

Q.

$\Delta ABCiscongruentto\Delta RQP$, that is $\Delta ABC\cong \Delta RQP$. If $\angle C$ and $\angle P$ are the smallest angles in $\Delta ABC$ and $\Delta RQP$, then $\angle P=?$

1. ∠A

2. ∠C

3. ∠B

4. Both ∠A and ∠B

Q.

In the given figure, if $\angle$ACB = ${30}^{\circ }$, the value of $\angle$ACD is .........

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${75}^{\circ }$

4. ${45}^{\circ }$

Q.

If $\Delta PQT\cong \Delta RSQ$, using RHS criterion, then

1. ∠TQP = ∠SQR

2. PQ = RS

3. PQ = RQ

4. PT = RS

Q. The distance between the two parallel lines is $1$ unit. A point '$A$' is chosen to lie between the lines at a distance '$d$' from one of them. Triangle $ABC$ is equilateral with $B$ on one line and $C$ on the other parallel line. Find the length of the side of the equilateral triangle is

1. $\frac{2}{3}\sqrt{d^2+d+1}$
2. $2\sqrt{\frac{d^2-d+1}{3}}$
3. $2\sqrt{d^2-d+1}$
4. $\sqrt{d^2-d+1}$

Q. Which congruence criterion do you use in the following?
Given: RP$=$ZX, RQ$=$ZY, $\angle$PRQ$=\angle$XZY. So $\Delta$PQR$\cong \Delta$XYZ.

Q. Triangle ABC is right angled at A. If AB = AC, then find the measures of angle B and angle C.

1. angle B = angle C = 90°
2. angle B = angle C = 65°
3. angle B = 35° and angle C = 55°
4. angle B = angle C = 45°

Q.

If $\Delta DEF\cong \Delta BCA$ , then the angle of $\Delta BCA$ that corresponds to $\angle E$ is _______ and side $FD$ corresponds to side ________.

1. $\angle A$, $BC$

2. $\angle C$, $AB$

3. $\angle B$, $AB$

4. Both $\angle C$​ and $\angle A$​, $BC$

Q.

In the below quadrilateral ABCD, if AD = BC and $\angle DAB$ = $\angle CBA$, then what is the relation between $\angle ABD$ and $\angle BAC$ ?

1. $\angle ABD$ = $\angle BAC$

2. $\angle ABD$ < $\angle BAC$

3. $\angle ABD$ > $\angle BAC$

4. $\angle DAB$ = $\angle BAC$

Q.

Given trapezium ABCD where $\Delta DAB\cong \Delta CBA$.

Which of the following options is true based on the given information?

1. $BD\cong CD$

2. $\angle BCE\cong \angle DAB$

3. $DA\cong DC$

4. $\angle ACB\cong \angle BDA$

Q. If $\Delta \text{XYZ}$ and $\Delta \text{ABC}$ are congruent, then which of the following is true?

1. XY = AB, YZ = BC and ZX = AC
2. Both the triangles can overlap
3. Area($\Delta \text{ABC})$ = Area($\Delta \text{XYZ})$
4. All of the above.

Q.

In $\Delta$ABC, $\angle$B = 50${}^{\circ }$. Find $\angle$A, if $\angle$B is congruent to $\angle$C.

1. 50${}^{\circ }$

2. 80${}^{\circ }$

3. 90${}^{\circ }$

4. 100${}^{\circ }$

Q. If triangles PQR and EFG are congruent , then angle R is equal to?

1. G
2. E
3. F
4. cannot be determined

Q.

Consider the figure below:

If AB = 5 cm; QR = 7cm; then find the value of AC (in cm.), if the perimeter of $△$ABC is 18cm.

___

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

1. 6 cm
2. 11 cm
3. 8 cm
4. 3 cm