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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?

Answer :

The student is not justified because there is not criterion for AAA congruence rule.

- Q.1 Which congruence criterion do you use in the following? (a) Given: AC = DF AB = DE BC = EF So, \(\triangle ABC \cong \triangle DEF \) (b) Given: 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.3 You have to show that \(\triangle AMP \cong \triangle AMQ \). In the fallowing proof, supply the missing reasons.
- 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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