Q 1 – Which congruence criterion do you use in the following?
(a) Given:
AC = DF
AB = DE
BC = EF
So, ∆ABC = ∆DEF
(b) Given:
ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ∆PQR ≅ ∆XYZ
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ∆LMN = ∆GFH
(d) Given:
EB = DB
AE = BC
∠A = ∠C = 90°
∆ABE = ∆CDB
Q 2 – You have to show that ∆AMP ≅ ∆AMQ. In the fallowing proof, supply the missing reasons.
| Steps | Reasons |
| (i) PM = QM | (i) |
| (ii) ∠PMA – ∠QMA | (ii) |
| (iii) AM = AM | (iii) |
| (iv) ∆AMP = ∆AMQ | (iv) |
Q 3 – In ∆ABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ∆PQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°.
A student says that ∆ABC = ∆PQR by AAA congruence criterion. Is he justified? Why or why not?
Q 4 – Draw a rough sketch of two triangles, such that they have five pairs of congruent parts but still the triangles are not congruent.
Q 5 – – In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆RAT ≅ ?
Q 6 –If ∆ABC and ∆PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
Q 7 – On the other square sheet, we have drawn two triangles ABC and PQR which are not congruent.
Such that
Q 8 – Complete the following statements:
(a) Two line segments are congruent if……..
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is…….
(c) When we write ∠A = ∠B, we actually mean….
Q 9 – Give any two real-life examples for congruent shapes.
Q 10 – Under a given correspondence, two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other.’
The above is known as
(a) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles
Q 11 – Under a given correspondence, two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle.’
The above is known as
(a) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles
Q 12 – Under a given correspondence, two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.’
The above is known as
(а) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles
Q 13 – Under a given correspondence, two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle.’
The above is known as
(а) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles
Q 14 – For two given triangles ABC and PQR, how many matchings are possible?
(a) 2
(b) 4
(c) 6
(d) 3
Q 15 – The symbol for congruence is
(a) ≡
(b) ≅
(c) ↔
(d) =
Q 16 – The symbol for correspondence is
(a) =
(b) ↔
(c) ≡
(d) ≅
Q 17 – If ∆ ABC = ∆ PQR, then ∠A corresponds to
(a) ∠P
(b) ∠Q
(c) ∠R
(d) none of these
Q 18 – If ∆ ABC = ∆ PQR, then ∠B corresponds to
(a) ∠P
(b) ∠Q
(c) ∠R
(d) none of these
Q 19 – If ∆ ABC= ∆ PQR, then ∠C corresponds to
(a) ∠P
(b) ∠Q
(c) ∠R
(d) none of these
Q 20 – We want to show that ∆ ART = ∆ PEN and we have to use SSS criterion. We have AR = PE and RT = EN. What more we need to show?
(a) AT = PN
(b) AT = PE
(c) AT = EN
(d) none of these
Q 21 – We want to show that ∆ ART = ∆ PEN. We have to use SAS criterion. We have ∠T = ∠N, RT = EN. What more we need to show?
(a) PN = AT
(b) PN = AR
(c) PN = RT
(d) None of these
Q 22 – We want to show that ∆ ART = ∆ PEN. We have to use ASA criterion. We have AT = PN, ∠A = ∠P. What more we need to show?
(a) ∠T = ∠N
(b) ∠T = ∠E
(c) ∠T = ∠P
(d) None of these
Q 23 – Which congruence criterion do you use in the following?
Given AC = DF
AB = DE
BC = EF
So, ∆ ABC ≅ ∆ DEF
(a) SSS
(b) SAS
(c) ASA
(d) RHS
Q 24 – Which congruence criterion do you use in the following?
Given : ZX = RP
RQ = ZY
∠ PRQ = ∠ XZY
So, ∆ PRQ = ∆ XYZ
(a) SSS
(b) SAS
(c) ASA
(d) RHS
Q 25 – Which congruence criterion do you use in the following?
(a) SSS
(b) SAS
(c) ASA
(d) RHS
Q 26 – Which congruence criterion do you use in the following?
(a) SSS
(b) SAS
(c) ASA
(d) RHS
Q 27 – In the following figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆ RAT = ?
(a) ∆ WON
(b) ∆ WNO
(c) ∆ OWN
(d) ∆ ONW
Q 28 – Complete the congruence statement ∆ BCA = ?
(a) ∆ BTA
(b) ∆ BAT
(c) ∆ ABT
(d) ∆ ATB
Q 29 – Complete the congruence statement ∆ QRS
(a) ∆ TPQ
(b) ∆ TQP
(c) ∆ QTP
(d) ∆ QPT
Q 30 – If ∆ ABC and ∆ PQR are to be congruent, name one additional pair of corresponding parts
(a) BC = QR
(b) BC = PQ
(c) BC = PR
(d) none of these
Q 31 – By which congruence, is ∆ ABC = ∆ FED?
(a) SSS
(b) SAS
(c) ASA
(d) RHS
Q 32 – Number of elements of a triangle is:
(a) 2
(b) 3
(c) 4
(d) 6
Q 33 – For two given triangles ABC and PQR, how many matching are possible?
(a) 2
(b) 3
(c) 4
(d) 6
Q 34 – Which of the following rules of congruency says that ∆ABC ≅ ∆PQR?
(a) ASA
(b) SAS
(c) SSS
(d) RHS