In each of the given pairs of triangles of Fig. 6.42, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
Solution:
Given, the figures represent different forms of triangles.
We have to apply ASA congruence criterion to each triangle.
We have to write the congruent triangles in symbolic form.
ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".
We observe that the side contained between the two angles are not equal.
Therefore, the triangles ABC and PQR are not congruent.
Two angles are equal. The side contained between the two angles are equal
i.e.,common side = DB
Therefore, ∆ABD ≅ ∆CBD
Two angles are equal.
The side contained between the two angles are equal. i.e.,4.8 units
Therefore, ∆XYZ ≅ ∆LMN
We observe that the side included between two equal angles are not equal.
Therefore, the triangle ABC and DEF are not congruent.
Two angles are equal.
The side contained between the two angles are equal.
I.e.,common side = NO
Therefore, ∆MNO ≅ ∆PON
Two angles are equal.
The side contained between the two angles are equal.
Therefore, ∆AOD ≅ ∆BOC
✦ Try This: In ∆PQR, if ∠P = 60°, and ∠Q = 40°, then the exterior angle formed by producing QR is equal to
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 134
In each of the given pairs of triangles of Fig. 6.42, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
Summary:
a) The triangles are not congruent, b) ∆ABD ≅ ∆CBD, c) ∆XYZ ≅ ∆LMN, d) The triangles are not congruent, e) ∆MNO ≅ ∆PON, f) ∆AOD ≅ ∆BOC
☛ Related Questions:
- In each of the given pairs of triangles of Fig. 6.43 ABCD, using only RHS congruence criterion, dete . . . .
- In each of the given pairs of triangles of Fig. 6.43 UXYZ, using only RHS congruence criterion, dete . . . .
- In each of the given pairs of triangles of Fig. 6.43 ABC, PQR, using only RHS congruence criterion, . . . .