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Question

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

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Solution

(i)
From the information shown in the figure,
in ABC and PQR
ABC PQR
seg BC seg QR
ACB PRQ
ABC PQR ....... ASA test
BAC QPR .......corresponding angles of congruent triangles.

seg AB seg PQ123Aand seg AC 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 ....... SAS test
TPQ TSRand TQP TRS...corresponding angles of congruent triangles

seg PQ seg SR corresponding sides of congruent triangles

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