Congruent Triangles

Q.

If two sides and one angle of a triangle are equal to the two sides and an angle of another triangle, then which of the following statement is correct?

1. True

2. False

3. They can be congruent only if the equal angle is included between the two corresponding equal sides

4. All are correct

Q.

Question 101

State whether the statement is True or False.

If two triangles are congruent, then the corresponding angles are equal.

Q.

Question 103

State whether the statement is True or False.

If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.

Q.

Question 1 (a)
Which congruence criterion do you use in the following?
Given AC = DF, AB = DE, BC = EF
So $\Delta ABC\cong \Delta DEF$

Q.

Question 91

State whether the statement is True or False.

Two right angles are congruent.

Q.

State true or false: If all the corresponding angles of two triangles are the same, then the two triangles are necessarily congruent.

1. True

2. False

Q. In the given congruent triangles under ASA, find the value of x and y, ΔPQR $\cong$ ΔSTU.

Q.

$△$ABC is congruent to $△$PQR. What is the perimeter of $△$PQR?

1. 12 cm

2. 13 cm

3. 14 cm

4. The length of at least one side of $△$PQR should be given

Q. Question 4
‘If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent; Is the statement true? Why?

Q.

In $\Delta ABCand\Delta PQR$, $AB=4cm,BC=5cm,AC=6cm$ and $PQ=4cm,QR=5cm,PR=6cm$, then which of the following is true?

1. ΔABC≅ΔRQP

2. ΔABC≅ΔQRP

3. ΔABC≅ΔPQR

4. ΔBAC≅ΔPQR

Q. By applying ASA congruence rule, it is to be established that ∆ABC ≅ ∆QRP and it is given that BC = RP. What additional information’s are needed to establish the congruence?

Q.

Question 102

State whether the statement is True or False.

If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent.

Q. If $\Delta ABC\text{and}\Delta PQR$ are congruent under the correspondence $ABC\leftrightarrow RPQ$, then the part of $\Delta ABC$ that correspond to $PQ$ is:

1. $AB$
2. None of the above
3. $BC$
4. $AC$

Q.

Question 142 (i)

Without drawing the triangles write all six pairs of equal measures in the given pair of congruent triangles.

$\Delta STU\cong \Delta DEF$

Q.

Question 63

Observe all the four triangles FAB, EAB, DAB and CAB as shown in the figure.

State whether the statement is True or False.

All triangles are congruent.

Q.

Question 4 (ii)
If $\Delta DEF\cong \Delta BCA$, write the part(s) of $\Delta BCA$ that corresponds to:
$\overline{EF}$

Q. $\Delta PQR$ is such that $\angle P=\angle Q=\angle R={60}^{\circ }$. Which of the following is true?

1. Both $A\text{and}B$
2. Neither $A\text{nor}B$
3. $\Delta PQR$ is an equilateral triangle.
4. $\Delta PQR$ is an acute-angled triangle.

Q.

Is it correct to say that two right angles are congruent? Give reasons.

Q.

Among two congruent angles, one has a measure of ${60}^o$, the measure of the corresponding angle of another triangle will be ___(in degrees).

Q. If three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

1. True
2. False

Q.

Question 100

State whether the statement is True or False.

If two sides and one angle of a triangle are equal to the two sides and angle of another triangle, then the two triangles are congruent.

Q. Which of the following statements are true (T) and which are false(F) :
Angles opposite to equal sides of a triangle are equal.

1. True
2. False

Q. Sum of all interior angle of a triangle is always less than ${180}^{\circ }$.

1. False
2. True

Q.

Rahul was trying to make a paper toy and started with folding an A4 sized paper along the diagonal. He then noticed that there were two triangles formed. Arjun was saying that the two triangles formed are congruent to each other. But then Rahul noticed that they aren’t superimposing on each other, he says that the triangles aren’t congruent.

What are the conditions for a triangle to be congruent?

1. Orientation of triangles does matter

2. Corresponding sides should be equal

3. Corresponding angles should be equal

4. Orientation of triangles does not matter

Q.

Question 61

Fill in the blanks to make the statement true.

Two rectangles are congruent if they have same ___ and ___.

Q. If three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

1. True
2. False

Q.

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

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

1. ∠BCE ≅ ∠DAB

2. BD ≅ CD

3. DA ≅ DC

4. ∠ACB ≅ ∠BDA

Q.

Question 42

If for $\Delta ABC$ and $\Delta DEF$, the correspondence $CAB\leftrightarrow EDF$ gives a congruence, then which of the following is not true?

a) AC = DE
b) AB = EF
c) $\angle A=\angle D$
d) $\angle C=\angle E$

Q. Which of the following is not a criterion for congruency of two triangles?

Q.

Question 4 (iii)
If $\Delta DEF\cong \Delta BCA$, write the part(s) of $\Delta BCA$ that corresponds to:
$\angle F$