Applications of Congruency

Q.

Are all equilateral triangles similar?

Q.

The difference of any two sides of a triangle is equal to the third side.

1. False

2. True

Q.

Line AB of 4 cm is drawn. Another line CD which is congruent and perpendicular to AB is drawn. Length of CD is_____.

1. 3 cm

2. 5 cm

3. 4 cm

4. 2 cm

Q. Two leaves of page from the same notebook are congruent.

1. True
2. False

Q. In $\Delta ABC$, if ∠A = 45° and ∠B = 65°, then the longest side of the triangle is .

1. AB
2. BC
3. CA

Q.

In $△$ABC, $\angle A={30}^{\circ }$ , $\angle B={40}^{\circ }$ and $\angle C={110}^{\circ }$.

In $△$PQR, $\angle P={30}^{\circ }$ , $\angle Q={40}^{\circ }$ and $\angle R={110}^{\circ }$.

Then the two triangles are necessarily congruent.

1. True

2. False

Q. Match the sides of the triangles in ascending order.

1. AB < AC < BC
2. AB < BC < AC
3. BC < AB < AC

Q. In a triangle ABC, ∠B = 90°, ∠C = 45°, ∠A=?

1. 45°
2. 50°
3. 55°
4. 65°

Q. ABC is a triangle such that $AB=10cm$ and $AC=3cm$. The side BC is

Q.

ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. [3 MARKS]

Q.

If all the corresponding angles of two triangles are same, then the two triangles are necessarily congruent.

1. True

2. False

Q.

What are the criteria for congruence of triangles?

1. SSS, SAS, ASA, AAS, RHS

2. SSS, SAS, ASS, AAS, RHS

3. SSS, SAS, ASA, SSA, RHS

4. SSS, SAS, ASA, AAS, AAA

Q.

Consider the two statements:

Statement 1: If two line segments have the same length, then they are congruent.

Statement 2: If two line segments are congruent, then they have the same length.

1. Statement 1 is true and statement 2 is false.

2. Statement 1 is false and statement 2 is true.

3. Both Statement 1 and statement 2 are true.

4. Both Statement 1 and statement 2 are false.

Q.

A rough sketch of two triangles is drawn. They have five pairs of congruent parts, but still the triangles are not congruent. True/False?

1. True

2. False

Q. The _____ of any two sides of a triangle is greater than the third side.

1. difference
2. sum of the product
3. sum
4. product