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Byju's Answer
Standard VIII
Mathematics
Congruency Postulates
State the tes...
Question

State the test by which both triangles are congruent to each other in the provided figure.

A
SSS
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B
ASA
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C
AAS
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D
SAS
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Solution

The correct option is D SAS
As given in the figure,
∠PRQ=∠TRS= Vertically opposite angle
PR=TR
SR=QR
△PRQ≅△TRS (by SAS)

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Q. In each of the examples given below, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same signs. Observe the figures and state the test by which the triangles in each pair are congruent.

(i)
By . . . . . . . . . . test
∆ABC ≅ ∆PQR

(ii)

By . . . . . . . . . . test
∆XYZ ≅ ∆LMN

(iii)

By . . . . . . . . . . test
∆LMN ≅ ∆PTR

(iv)

By . . . . . . . . . . test
∆LMN ≅ ∆ PTR
Q. In pair of triangle in the following figure, parts bearing identical marks are congruent. State the test and correspondence if vertices by which triangle in each pair are congruent.
1352725_98bca8e307b24c80b828bec4e0cc753d.png
Q.

In each pair of triangles in the following figures, parts bearing indentical marks are congruent. State the test and correspondence of vertices by which triangles in each pair are congruent.
(i)

(ii)

(iii)

(iv)

(v)

Q.
Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

(i)

From the information shown in the figure,
in ∆ABC and ∆PQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB≅ ∠PRQ
∴ ∆ABC ≅ ∆PQR ....... 3243432 test
∴ ∠BAC ≅ 3243432 .......corresponding angles of congruent triangles.

seg AB≅ 1234and 1234 ≅ seg PR...corresponding sides of congruent triangles


(ii)

From the information shown in the figure,
in ∆PTQ and ∆STR
seg PT ≅ seg ST
∠PTQ≅ ∠STR...... vertically opposite angles
∴ ∆PTQ ≅ ∆STR ....... 3243432 test
∴ ∠TPQ≅ 1234and 1234 ≅ ∠TRS...corresponding angles of congruent triangles

seg PQ ≅ 3243432 corresponding sides of congruent triangles
Q. In each pair of triangles given below, parts shown by identical marks are congruent. State the test and the one to one correspondence of vertices by which triangles in each pair are congruent and remaining congruent parts.
(1)


(2)

(3)
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