NCERT solutions of related questions for Congruence of Triangles
- Q.1 Which congruence criterion do you use in the following?
AC = DF
AB = DE
BC = EF
So, \(\triangle ABC \cong \triangle DEF \)
ZX = RP
RQ = ZY
\(\angle PRQ = \angle XZY \)
So, \(\triangle PQR \cong \triangle XYZ \)
(c) Given: \(\angle MLN = \angle FGH \)
\(\angle NML = \angle GFH \)
ML = FG
So, \(\triangle LMN \cong \triangle GFH \)
(d) Given: EB = DB
AE = BC
\(\angle A = \angle C = 90° \)
So, \(\triangle ABE \cong \triangle CDB \)
- Q.2 You want to show that \(\triangle ART = \triangle PEN, \)
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ?T = ?N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?
- Q.4 In ?ABC, \(\angle A = 30° \angle B = 40° and \angle C = 110° \)
In \(\triangle PQR, \angle P = 30°, \angle Q = 40° and \angle R = 110°.\)
A student says that \(\triangle ABC = \triangle PQR \) by AAA congruence criterion.
Is he justified? Why or why not?
- Q.5 In the figure, the two triangles are congruent. The corresponding parts are marked. We can write \(\triangle RAT \cong \) ?
- Q.6 Complete the congruence statement:
\(\triangle BCA \cong ?
\triangle QRS \cong ? \)
- Q.7 In a squared sheet, draw two triangles of equal areas such that:
(i) the triangles are congruent.
(ii) the triangle are not congruent.
What can you say about their perimeters?
- Q.8 Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.
- Q.9 If \(\triangle ABC and \triangle PQR \) are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
- Q.10 Explain, why \(\triangle ABC \cong \triangle FED \)
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