Congruent Triangles

Q.

In each pair of triangles in the following figures, parts bearing indentical marks are congruent. State the test and correspondence of vertices by which triangles in each pair are congruent.
(i)

(ii)

(iii)

(iv)

(v)

Q.

If $\Delta ABC\cong \Delta PQR,$ then AB is equal to ___.

1. PR

2. QR

3. PQ

4. Both PR and QR

Q. The only condition required for two polygons to be similar is that their corresponding angles should be equal.

1. True
2. False

Q. If triangles ABC and DEF shown below are congruent then length of side DF is.

1. 3
2. 4
3. 5

Q.

What are Congruences?

Q.

Which of the following is not a criterion for congruence of triangles?

1. SAS

2. ASA

3. SSA

4. SSS

Q. In two triangles, three angles of one triangle are correspondingly equal to the three angles of the another triangle.
Which of the following statements is correct?

1. Both triangles may be congruent or may not be congruent.
2. The two triangles can never be congruent
3. The two triangles must be congruent
4. None of the above

Q. Prove that in an isosceles triangle the perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

Q. Find the length of the side $PR$ and $QR$ if the $△ABC$ is similar to $△PQR$ and $\frac{AB}{PQ}=\frac{AC}{PR}$

1. $PR=3,QR=1$
2. $PR=4,QR=2$
3. $PR=4,QR=1.5$
4. $PR=6,QR=3$

Q. We can construct infinite equilateral triangles having different length of sides.

1. False
2. True

Q. Which of the following is not a congruence criterion?

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

Q. Two congruent triangles, $△ABCand△PQR$ can be symbolically represented as:

1. $△ABC\equiv △PQR$
2. $△ABC\cong △PQR$
3. $△ABC=△PQR$
4. None of the above

Q. If the triangles given in the adjoining figure are congruent to each other, find the value of $x$.

1. $3$
2. $4$
3. $5$
4. None of the above

Q. For two given triangles, if two of their angles are equal the triangles will be similar.

1. True
2. False

Q.

Which congruency criterion could be used only to check for congruency of two right-angled triangles?

1. ASA congruency

2. SAS congruency

3. RHS congruency

4. SSS congruency

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. What are the corresponding parts of the figures below? Choose the appropriate pairs
.

1. FG
2. XV
3. GE
4. VW
5. EF
6. WX
7. $\angle F$
8. $\angle E$
9. $\angle V$
10. $\angle X$

Q. We can construct infinite equilateral triangles having different length of sides.

1. False
2. True

Q. The radius of a circle is increased by $2$ cm from $5$ cm to $7$ cm. Find the increase in area?

Q. are kites rhombuses parallelogram said to be quadrilaterals because all of them have four sides or is there any more reason

Q. If the two triangles $ABC$ and $PQR$ are similar and $x:y=1:2$, then

1. $x=22°,y=44°$
2. $x=22°,y=88°$
3. $x=44°,y=22°$
4. $x=44°,y=88°$

Q. You have to show that $\Delta AMP\cong \Delta AMQ$. In the following proof, supply the missing reasons:
$\begin{array}{cc}Steps& Reasons\\ i)PM=QM& \left(i\right)\\ ii)\angle PMA=\angle QMA& \left(ii\right)\\ iii)AM=AM& \left(iii\right)\\ iv)\Delta AMP\cong \Delta AMQ& \left(iv\right)\end{array}$

Q. In $\Delta ABC,AB=AC$ and $AD\perp BC$. Then the line of symmetry is

1. $AB$
2. $AC$
3. $BD$ and $DC$
4. $AD$

Q. State whether the following statemnt is true or false.
If two triangles are equal in perimeter, they must be congruent.

Q. $△ABC\cong △PQR$.
Which of the following are correct?

1. $AB=PQ$
2. $AC=QR$
3. $m\angle A=$ $m\angle R$
4. $m\angle B=$ $m\angle Q$

Q. If $\Delta ABC\sim \Delta DFE,\angle A={30}^{\circ },\angle C={50}^{\circ },$ $AB=5cm,AC=8cm,andDF=7.5cm$ , then which of the following is true?

(A) $DE=12cm,\angle F={50}^{\circ }$
(B) $DE=12cm,\angle F={100}^{\circ }$
(C) $EF=12cm,\angle D={100}^{\circ }$
(D) $EF=12cm,\angle D={30}^{\circ }$

Q.

Two regular polygons each having $7$ sides are ____________ (Similar/Not Similar)

Q. We can construct infinite equilateral triangles having different length of sides.

1. False
2. True

Q.

In the given figure, $AD=BC.$ What is the length of $AB$ if $DC=4cm?$

1. 5 cm

2. 4 cm

3. 3 cm

4. Can’t find

Q. If $\Delta ABC\sim \Delta DFE,\angle A={30}^{\circ },\angle C={50}^{\circ },$ $AB=5cm,AC=8cm,andDF=7.5cm$ , then which of the following is true?

(A) $DE=12cm,\angle F={50}^{\circ }$
(B) $DE=12cm,\angle F={100}^{\circ }$
(C) $EF=12cm,\angle D={100}^{\circ }$
(D) $EF=12cm,\angle D={30}^{\circ }$