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Question
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
in ΔPTQ and ΔSTR
seg PT ≅ seg ST
∠PTQ ≅ ∠STR ...[Vertically opposite angles]
∴ ΔPTQ ≅ ΔSTR ...`square` test
∴ `{:("∠TPQ" ≅ square),("and" square ≅ "∠TRS"):}}` ...corresponding angles of congruent triangles
seg PQ ≅ `square` ...corresponding sides of congruent triangles
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Solution
From the information shown in the figure, in ΔPTQ and ΔSTR
seg PT ≅ seg ST
∠PTQ ≅ ∠STR ...Vertically opposite angles
∠PTQ ≅ ∠STR ...SAS test
∴ `{:("∠TPQ" ≅ bbunderline("∠TSR")),(bbunderline("∠TQP")≅ "∠TRS"):}}` ...[corresponding angles of congruent triangles]
seg PQ ≅ seg SR ...[corresponding sides of congruent triangles]
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