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.

Answer 1

From the information shown in the figure,
$\text{in}△PTQ\text{and}△STR$
$\text{seg}PT\cong \text{seg}ST$
$\angle PTQ\cong \angle STR$ ...... (vertically opposite angles)
$\text{seg}PT\cong \text{seg}ST$
$\therefore △PTQ\cong △STR$ (By SAS rule)
$\therefore \angle TPQ\cong \angle TSR\text{and}\angle TQP\cong \angle TRS$ .
(corresponding angles of congruent triangles)
$\text{seg}PQ\cong \text{seg}SR$
( corresponding sides of congruent triangles)