GSEB Class 7 Maths Solutions Chapter 7 Congruence of Triangles Exercise 7.1

GSEB Solutions

Question 1. Complete the following statements:
(a) Two line segments are congruent
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is.
(c) When we write \( \angle A = \angle B \), we actually mean
Answer:
(a) Two line segments are congruent if they possess the same length.
(b) Among two congruent angles, if one measures 70°, the measurement of the other angle will also be 70°.
(c) When we express \( \angle A = \angle B \), we are actually implying that their measures are equal, i.e., \( m \angle A = m \angle B \).
In simple words: Congruent shapes are identical in size and form. This means that if two line segments are congruent, they must have the same length. Similarly, if two angles are congruent, their measurements are exactly the same. When we say angles are equal, we mean their measures are equal.

Exam Tip: Remember that "congruent" means identical in shape and size. For line segments, this means equal length; for angles, it means equal measure.

Question 2. Give any two real-life examples for congruent shapes.
Answer:
(i) Shaving blades from the identical brand.
(ii) Biscuits of the same kind found within the same packet.
In simple words: Things that are exactly the same in shape and size are congruent. Think of identical items made in a factory, like coins or fresh cookie cutters.

Exam Tip: To score full marks, provide examples where objects are perfectly interchangeable, highlighting that they have both the same shape and size.

Question 3. If \( \triangle ABC = \triangle FED \) under the correspondence ABC \( \leftrightarrow \) FED, write all the corresponding congruent parts of the triangles.
Answer: All the matching congruent parts for \( \triangle ABC \) and \( \triangle FED \) are:
\( \angle A \leftrightarrow \angle F \)
\( \angle B \leftrightarrow \angle E \)
\( \angle C \leftrightarrow \angle D \)
\( \overline{AB} \leftrightarrow \overline{FE} \)
\( \overline{BC} \leftrightarrow \overline{ED} \)
\( \overline{CA} \leftrightarrow \overline{DF} \)
In simple words: When two triangles match perfectly, their corners and sides that line up are exactly the same. So, Angle A matches Angle F, Side AB matches Side FE, and so on, for all three pairs of angles and all three pairs of sides.

Exam Tip: When writing corresponding parts, make sure the order of vertices in the correspondence (e.g., ABC \( \leftrightarrow \) FED) directly indicates which angles and sides match up.

Question 4. If \( \triangle DEF = \triangle BCA \), write the part(s) of \( \triangle BCA \) that corresponding to
(i) \( \angle E \)
(ii) \( \overline{EF} \)
(iii) \( \angle F \)
(iv) \( \overline{DF} \)
Answer: Since \( \triangle DEF \cong \triangle BCA \), the corresponding parts of \( \triangle BCA \) are:
(i) \( \angle E \leftrightarrow \angle C \)
(ii) \( \overline{EF} \leftrightarrow \overline{CA} \)
(iii) \( \angle F \leftrightarrow \angle A \)
(iv) \( \overline{DF} \leftrightarrow \overline{BA} \)
In simple words: If two triangles are congruent, their matching angles and sides are equal. For example, if angle E in the first triangle lines up with angle C in the second, they are the same. The same applies to corresponding sides like EF and CA.

Exam Tip: Pay close attention to the order of vertices in the congruence statement, as this directly determines the corresponding parts.