CBSE Class 7 Mathematics Congruence Of Triangles Worksheet Set 02

Question 1. Study the following pairs of triangles in each case and identify the congruent parts [Use ASA congruence].
Answer:
Based on the given figures and using the ASA (Angle-Side-Angle) congruence criterion, the corresponding congruent parts for each pair of triangles are identified as follows:

(a) For triangles in figure (a):
i) \(\angle TSA\) corresponds to \(\angle LEG\)
ii) Side \(\text{SA}\) corresponds to side \(\text{EG}\)
iii) \(\angle TAS\) corresponds to \(\angle LGE\)

(b) For triangles in figure (b):
i) Side \(\text{HD}\) corresponds to side \(\text{TE}\)
ii) \(\angle HWD\) corresponds to \(\angle TES\)
iii) \(\angle HDW\) corresponds to \(\angle TSE\)

(c) For triangles in figure (c):
i) \(\angle GLA\) corresponds to \(\angle PGB\) (or appropriate corresponding angles based on orientation)
ii) \(\angle LAG\) corresponds to \(\angle PBG\)
iii) Side \(\text{LA}\) corresponds to side \(\text{BG}\)
In simple words: Corresponding parts of congruent triangles match each other in terms of equal angles and equal side lengths according to the ASA rule.

Exam Tip: Always match the vertices in the correct order of correspondence (e.g., if \(\triangle STA \cong \triangle LEG\), then vertex S corresponds to L, T to E, and A to G).

Question 2. Name the pairs of congruent parts using the ASA congruence in the following pairs of triangles:
Answer:
(a) For figure (a) with triangles \(\triangle ABC\) and \(\triangle DEF\):
i) Angle pair: \(\angle B = \angle E\)
ii) Included side pair: \(\text{BC} = \text{EF}\)
iii) Angle pair: \(\angle C = \angle F\)
Therefore, by ASA congruence, \(\triangle ABC \cong \triangle DEF\).

(b) For figure (b) with triangles \(\triangle TIK\) and \(\triangle TES\):
i) Angle pair: \(\angle ITK = \angle ETS\) (vertically opposite angles)
ii) Side pair: \(\text{TK} = \text{TE}\) (given equal sides)
iii) Angle pair: \(\angle IKT = \angle EST\)
Therefore, by ASA congruence, \(\triangle TIK \cong \triangle TES\).
In simple words: ASA congruence requires two angles and the side included between them to be equal in both triangles.

Exam Tip: The side must always be the included side between the two given angles to correctly apply the ASA criterion.

Question 3. Study the pairs of triangles and prove that i) \(\triangle ABC \cong \triangle DEF\) ii) \(\triangle KQC \cong \triangle CQJ\) iii) \(\triangle HJP \cong \triangle MOL\) iv) \(\triangle BAG \cong \triangle BAL\).
Answer:
i) Proof for \(\triangle ABC \cong \triangle DEF\):
In \(\triangle ABC\) and \(\triangle DEF\):
\(\angle B = \angle E\) (given)
Side \(\text{BC} = \text{EF}\) (given)
\(\angle C = \angle F\) (given)
Therefore, by ASA congruence criterion, \(\triangle ABC \cong \triangle DEF\).

ii) Proof for \(\triangle KQC \cong \triangle CQJ\):
In \(\triangle KQC\) and \(\triangle CQJ\):
\(\angle KQC = \angle CQJ = 90^\circ\) (given right angles)
Side \(\text{QC} = \text{CQ}\) (common side)
\(\angle KCQ = \angle QCJ\) (given equal angles)
Therefore, by ASA congruence criterion, \(\triangle KQC \cong \triangle CQJ\).

iii) Proof for \(\triangle HJP \cong \triangle MOL\):
In \(\triangle HJP\) and \(\triangle MOL\):
\(\angle HJP = \angle MOL\) (given)
Side \(\text{JP} = \text{OL}\) (given)
\(\angle HPJ = \angle OLM\) (given)
Therefore, by ASA congruence criterion, \(\triangle HJP \cong \triangle MOL\).

iv) Proof for \(\triangle BAG \cong \triangle BAL\):
In \(\triangle BAG\) and \(\triangle BAL\):
\(\angle ABG = \angle ABL\) (given)
Side \(\text{AB} = \text{AB}\) (common side)
\(\angle BAG = \angle BAL\) (given)
Therefore, by ASA congruence criterion, \(\triangle BAG \cong \triangle BAL\).
In simple words: State the two angles and the included side that are equal in both triangles to prove they are congruent.

Exam Tip: Clearly write the three conditions (two angles and one side) in proper order before stating the congruence rule.

Question 4. Given that the following pairs of triangles are congruent to each other by the ASA congruency fill in the blanks:
Answer:
i) For figure (a):
a) \(\angle PRS = \angle QRS = 30^\circ\)
b) \(\text{RS} = \text{RS}\) (common side)

ii) For figure (b):
Fill up the correct measures:
a) \(\angle PMS = 40^\circ\)
b) \(\text{MS} = 7\text{ cm}\)
c) \(\angle MSP = 50^\circ\)
Which condition of congruence is satisfied here? ASA congruence condition is satisfied here.
In simple words: Corresponding parts of congruent triangles (CPCT) are equal, and common sides have equal lengths in both triangles.

Exam Tip: Remember that when two triangles are proven congruent, all their corresponding sides and angles are automatically equal.

Please refer to attached file for CBSE Class 7 Maths Worksheet - Congruence of Triangles (2)