Question

State 'T' for true and 'F' for false.
1. To examine the congruence of plane figures, the superposition method is used.
2. If two-line segments have different lengths, they are congruent.
3. The measure of two congruent angles is the same.
4. Objects which are exact copies of one another are called plane objects.
5. If the corresponding angles of two triangles are equal, the triangles are said to be congruent.

Order of true false of above statements is
A. ${\text{T T T F F}}$
B. ${\text{T T F T F}}$
C. ${\text{T F T F F}}$
D. ${\text{T F T T T}}$

Answer 1

Hint: Define the term congruence. Check the validity of the statements in the problem in order with respect to the definition of congruence.

Complete step-by-step answer:

Given in the problem we need to state ‘T' for true and 'F' for false for the given statements from 1 to 5.
Let us examine the statements one by one.

Statement 1: To examine the congruence of plane figures, the superposition method is used.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Therefore, by superposition or overlapping, one can examine the congruence of plane figures.
Hence statement 1 is true.

Statement 2: If two-line segments have different lengths, they are congruent.
If the line segments have different lengths, they cannot overlap each other. Hence, they are not congruent.
Statement 2 is false.

Statement 3: The measure of two congruent angles is the same.
If two angles are equal, they will overlap each other when superimposed, hence are congruent.
Statement 3 is true.

Statement 4: Objects which are exact copies of one another are called plane objects.
From the definition of congruence above, the objects which are exact mirror copies of one another are called congruent.
Hence statement 4 is false.

Statement 5: If the corresponding angles of two triangles are equal, the triangles are said to be congruent.
The above condition is valid for similarity of the two triangles, but for congruence the triangles should superimpose each other which will require a side between the two equal corresponding angles to be the same in addition.
Hence statement 5 is false.

From the above analysis the correct answer is (C). ${\text{T F T F F}}$.

Note: The distinction between conditions of congruence and similarity should be kept in mind while attempting problems like above. The congruence could be verified by drawing the planar figures in addition to verbal argument.