Congruent Triangles

Q. Any two triangles are said to be congruent if

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

Q.

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

1. PR

2. QR

3. PQ

4. Both PR and QR

Q.

There is a park with two triangular jogging tracks. Rahul and Arjun went for jogging. The park had a route map which mentioned that the sides of jogging tracks with the same colour have the same length and nothing was mentioned about different coloured sides.

Which of the following is true?

1. Black track = Green track
2. Red track = Green track
3. Black track = Red track
4. Blue track = Green track

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.

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. $\angle B$, $AB$

3. $\angle C$, $AB$

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

Q.

Two triangles are congruent if they have

1. Same name

2. Equal measures

3. Unequal measures

4. Same direction

Q.

Consider the figure below.

If $\angle A={50}^{\circ }$, and $\angle Q={60}^{\circ }$, then find the value of $\angle B$ (in degrees).

___

Q.

If $\Delta ABC\cong \Delta RQP$ , then $\angle P$ = _____ .

1. $\angle A$

2. $\angle C$

3. $\angle B$

4. Both $\angle A$ and $\angle B$

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. 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.