Solved MCQs: Congruence Criteria- SAS And ASA | Mathematics (Maths) Class 9 PDF Download

Q1: In the given figure, AB = AC, AD = AE = 5 cm and DC = 8 cm. Length of EB is______. 

(a) 3 cm
(b) 8 cm
(c) 7 cm
(d) 5 cm
Ans: b
Sol: 8 cm is the answer because DC = EB = 8 cm.

Q2: Triangle ABC is congruent to triangle DEF. Which side is congruent to side BC?
(a) DE
(b) DF
(c) EF
(d) none of the above
Ans: c
Sol: The side BC is congruent to side EF.

Q3: Which of the following statements is incorrect ?
(a) Two squares having the same side length are congruent
(b) Two rectangles having the same area are congruent
(c) Two circles having the same radius are congruent
(d) Two lines having same length are congruent
Ans: b
Sol: 2 rectangles having same area may differ in their lengths. So they will not be congruent

Q4: In the following figure, PQ = PR and SQ = SR, then 

(a) ∠PQS =∠PRS
(b) ∠PQS = ∠PQR
(c) ∠PQR = ∠SQR
(d) ∠PRQ = ∠SRQ
Ans: a
Sol: In △PQR and △SRQ,
► PQ = SR(Given)
► QR = QR(Common)
► PR = SQ(Given)
By SSS property:
△PQR≅△SRQ
Therefore, ∠PQS =∠PRS

Q5: If two triangles ABC and PQR are congruent under the correspondence A ↔ P, B ↔ Q and C ↔ R, then symbolically, it is expressed as
(a) ΔABC ≅ ΔPQR
(b) ΔABC = ΔPQR
(c) ΔABC and ΔPQR are scalene triangles
(d) ΔABC and ΔPQR are isosceles triangles
Ans: a

Q6: If ΔABC ≌ ΔPQR then, which of the following is true?
(a) CA = RP
(b) AB = RP
(c) AC = RQ
(d) CB = QP
Ans: a
Sol: Corresponding sides in congruent triangles are equal.
So AC = PR ,AB = PQ ,BC = QR

Q7: If two sides of a triangle are equal, the angles opposite to these sides are______. 

(a) supplementary
(b) equal
(c) right angles
(d) not equal
Ans: b
Sol: Theorem: Angles opposite to equal sides of an isosceles triangle are equal.

Q8: In case of two equilateral triangles, PQR and STU which of the following correspondence is not correct?

(a) PQR ↔ TTS
(b) PQR ↔ STU
(c) PQR ↔ SUT
(d) PQR ↔ UST
Ans: a
Sol: 
The correct option is Option A.
All equilateral triangles have the same angles by the congruence rule (SSS)
So, TTS <—> PQR

Q9: In quadrilateral ADBC, AB bisects ∠A. Which of the following criterion will prove ΔABC ≅ ΔABD?

 
(a) AD = BC , ∠CAB = ∠BAD , AB = AB
(b) ∠CBA = ∠CAB , AC = BC , ∠ACB = ∠ACB
(c) AC = BD , ∠ACB = ∠ADB , AB = AB
(d) AC = AD , ∠CAB = ∠DAB , AB = AB
Ans: d
Sol: In quadrilateral ADBC we have:
► AC = AD
and AB being the bisector of ∠A.
Now, in ΔABC and ΔABD:
► AC = AD     [Given]
► AB = AB     [Common]
► ∠CAB = ∠DAB [∴ AB bisects ∠CAD]
∴ Using SAS criteria, we have
ΔABC ≌ ΔABD.
∴ Corresponding parts of congruent triangles (c.p.c.t) are equal.
∴ BC = BD

Q10: In an isosceles triangle ABC with AB = AC, if BD and CE are the altitudes, then BD and CE are______.

 
(a) perpendicular to each other.
(b) not equal to each other.
(c) equal to each other.
(d) parallel to each other.
Ans: c
Sol: Given: △ABC, AB=AC, BD⊥AC and CE⊥AB
Area of triangle = 1/2 × base × height
Area of △ABC = 1/2 × AB × CE = 1/2 × BD × AC
CE = BD (Since, AB=AC)

Q11: In fig., if AB = AC and PB = QC, then by which congruence criterion PBC ≅ QCB 

(a) SSS
(b) RHS
(c) ASA
(d) SAS
Ans: d
Sol: As AB = AC so angle ACB = angle(ABC) as angles opposite to equal sides r equal.
In triangle PBC and Triangle QCB we see that:
i) PB = QC (given)
ii) angle(PBC) = (angle)QCB (proved earliar)
iii) BC = BC (common)
So, triangle PBC is congruent to triangle QCB by SAS axiom of congruency.

Q12: The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then 

(a) PS = PQ and QR = RS
(b) PS = PR and SR = QS
(c) PQ = SR and QR = PS
(d) PS = RS and PQ = QR
Ans: a
Sol: 
In Δ PSR and ΔPQR
► PR = PR
► ∠ 1 = ∠ 2
► ∠ 3 = ∠ 4
Δ PSR ≅ Δ PQR  [ASA]
► PS = PQ   [CPCT]
► QR = RS  [CPCT]
The correct option is Option A

Q13: In the given figure, AB = EF, BC = DE, AB ⊥ BD and EF ⊥ CE. Which of the following criterion is true for ΔABD ≅ ΔEFC? 

(a) AAS
(b) ASA
(c) SSS
(d) SAS
Ans: d
Sol: In triangle ABD and FEC:
► AB = FE ( given )
► ∠FEC = ∠ABD ( 90degree)
► BC = DE
CD is common part coming in both triangles.
► BC + CD = CD + DE
► BD = CE
Therefore, triangle ABD is congruent to triangle FEC by SAS rule of congruence.

Q14: Two figures are congruent if they have______.
(a) same area
(b) same size
(c) same shape
(d) same shape and size
Ans: d
Sol: In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Q15: A triangle can have______.
(a) Two obtuse angles
(b) Two acute angles
(c) Two right angles
(d) All angles more than 60°
Ans: b
Sol: The least number of acute angles that a triangle can have is 2.
As we cannot have more than one right angle or obtuse angle, we have only two or three acute angles in a triangle.
Further, if one angle is acute, sum of other two angles is more than 90⁰ and we cannot have two right angles or obtuse angles.