1In triangle ABC and triangle PQR, \( AB = PQ \), \( BC = QR \) and \( CA = RP \). On what basis are they congruent?
2In triangle ABC and triangle XYZ, \( \angle ABC = \angle XYZ \), \( BC = YZ \) and \( \angle ACB = \angle XZY \). On what basis are they congruent?
3In triangle ABC and triangle DEF, \( \angle ABC = \angle DEF = 90^\circ \), \( \angle BAC = \angle EFD \) and \( BC = ED \). On what basis are they congruent?
4In triangle ABC and triangle PQR, \( \angle ABC = \angle PQR = 90^\circ \), \( AC = PR \) and \( BC = QR \). On what basis are they congruent?
5If \( \triangle ABC \cong \triangle PQR \), write down the corresponding angles and the corresponding sides.
6Which three pairs of corresponding sides must be equal to make triangle ABC and triangle PQR congruent?
7D is the midpoint of the line AB and \( CD \perp AB \). Show that \( \triangle ACD \) and \( \triangle BCD \) are congruent.
8Given \( \angle RPQ = \angle PQS \) and \( QS = PR \), prove that \( \triangle PQR \) and \( \triangle QPS \) are congruent.
9In \( \triangle ABC \) and \( \triangle PQR \), \( \angle BAC = \angle QPR \) and \( \angle ABC = \angle PQR \). What further condition makes \( \triangle ABC \cong \triangle PQR \)?
10Given \( \angle LMN = \angle YXZ = 90^\circ \) and \( MN = XZ \). What further condition makes \( \triangle LMN \) and \( \triangle XYZ \) congruent, and by which test?
11If the corresponding sides of \( \triangle IJK \) and \( \triangle PQR \) are in the ratio \( 1 : 1 \), what kind of triangles are they?
12Two similar triangles have corresponding sides of 3 cm and 12 cm. What is their ratio?
13\( \triangle ABC \sim \triangle DEF \) with \( AB = 5 \) cm, \( AC = 3 \) cm, \( DE = 10 \) cm and \( EF = 12 \) cm. Find BC and DF.
14\( \triangle ABC \sim \triangle PQR \) with \( \angle A = \angle P = 60^\circ \), \( \angle B = \angle Q = 70^\circ \), \( AB = 2 \) cm, \( AC = 6 \) cm, \( PQ = 3 \) cm and \( QR = 6 \) cm. Find BC and PR.
15\( \triangle PQR \sim \triangle XZY \) with \( \angle X = 85^\circ \), \( \angle Y = 75^\circ \), \( QR = 8 \) cm, \( ZY = 16 \) cm and \( XY = 8 \) cm. Find the ratio of corresponding sides, the value of \( \angle PQR \) and the length of PR.
16Why are two triangles with all three angles equal not always congruent?
17One triangle has sides 5 cm, 6 cm and 7 cm, and another triangle also has sides 5 cm, 6 cm and 7 cm. Are they congruent, and on what basis?
18Two similar triangles have corresponding sides in the ratio \( 2 : 3 \). If one side of the smaller triangle is 6 cm, how long is the corresponding side of the larger triangle?
19Is the statement that every pair of congruent triangles is also similar true or false? Give a reason.