Chapter 7: Triangles

Choose the correct answers

Q1. If ∆ABC≅∆PQR and ∆ABC is not congruent to ∆PQR , then which of the following is not true :

(A) BC = PQ     (B) AC = PR   (C) QR = BC  (D) AB = PQ

Ans : (A) BC = PQ

Q2. Which of the following is not a criterion for congruence of triangles ?

(A) SAS      (B) ASA     (C) SSA      (D) SSS

Ans : (C) SSA

Q3. If AB = QR , BC = PR and CA = PQ , then

(A) ∆ABC≅∆PQR         (B)  ∆CBA≅∆PRQ    

(C)  ∆BAC≅∆RPQ      (D)  ∆PQR≅∆BCA

Ans: (B)  ∆CBA≅∆PRQ .

Q4. In ∆ABC , AB = AC and ∠B=50° . Then ∠C is equal to :

(A) 40°                      (B) 50°   

(C) 80°                      (D)  130°

Ans :  (B) 50°

[Hints:  Since, ∆ABC is an isosceles triangle .

        ∠B=∠C=50°  ]

Q5. In ∆ABC , BC = AB and ∠B=80° . Then ∠A is equal to :

(A) 80°     (B) 40°    (C) 50°     (D)  100°

Ans:  (C) 50°

 [ Hints:  In ∆ABC , we have

∠A+∠B+∠C=180° 

⇒∠A+80°+∠A=180° 

⇒2∠A=180°-80°=100° 

⇒∠A=100°2=50° ]

Q6. In ∆PQR ,∠R=∠P and QR = 4 cm and PR = 5 cm . Then the length of PQ is :

(A) 4 cm     (B) 5 cm       (C) 2 cm   (D) 2.5 cm

Ans : (A) 4 cm  . 

[ Hints: In∆PQR ,∠R=∠P

PQ=QR=4 cm ]

Q7. D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC . Then

(A) BD = CD              (B) BA > BD   

(C) BD > BA               (D) CD > CA 

Ans: (B) BA > BD .

Q8. It is given that ∆ABC≅∆FDE and AB = 5 cm , ∠B=40° and ∠A=80° . Then which of the following is true ?

(A) DF = 5 cm , ∠F=60°          (B) DF = 5 cm , ∠E=60° 

(C) DE = 5 cm , ∠E=60°           (D) DF = 5 cm , ∠D=60° 

Ans : (B) DF = 5 cm , ∠E=60° .

Q9. Two sides of a triangle are of lengths 5 cm and 1.5 cm . The length of the third side of the triangle cannot be :

(A) 3.6 cm     (B) 4.1 cm     (C) 3.8 cm     (D) 3.4 cm

Ans:  (D) 3.4 cm

[Hints:  1.5 + 3.6 = 5.1 > 5  ; 1.5 + 4.1 = 5.6 > 5  ; 1.5 + 3.8 = 5.3 > 5  ; 1.5 +3.4 = 4.9 < 5 ]

Q10.  In ∆PQR , if ∠R>∠Q , then

(A) QR > PR     (B) PQ > PR     (C) PQ < PR    (D) QR < PR   

Ans: (B) PQ > PR  .