Class 9 Mathematics MCQ Triangles

Question : Which of the following is not a criterion for congruence of triangles?
(a) SAS
(b) ASA
(c) SSA
(d) SSS

Question : In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are
(a) Isosceles and congruent
(b) Isosceles but not congruent
(c) Congruent but not isosceles
(d) Neither congruent nor isosceles

Question : In ∆ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is
(a) 2 cm
(b) 2.5 cm
(c) 4 cm
(d) 5 cm

Question : If AB = QR, BC = PR and CA = PQ, then
(a) ∆ PQR ≅ ∆ BCA
(b) ∆ BAC ≅ ∆ RPQ
(c) ∆ CBA ≅ ∆ PRQ
(d) ∆ ABC ≅ ∆ PQR

Question : If ∆ ABC ≅ ∆ PQR, then which of the following is not true?
(a) AC = PR 
(b) BC = PQ
(c) QR = BC
(d) AB = PQ

Question : In ∆ ABC, BC = AB and ∠B = 80°. Then ∠A is equal to
(a) 40°
(b) 50°
(c) 80°
(d) 100°

Question : 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) 3.4 cm
(b) 3.6 cm
(c) 3.8 cm
(d) 4.1 cm

Question : In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to
(a) 40°
(b) 50°
(c) 80°
(d) 130°

Question : In ∆ PQR, if ∠R > ∠Q, then
(a) QR < PR 
(b) PQ < PR
(c) PQ > PR
(d) QR > PR 

Question : 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) DE = 5 cm, ∠D = 40

Question : In the given figure, ΔABC ~ ΔDCB, then
AB × DB =
(a) OA × OD 
(b) OB × OC
(c) AB × DC
(d) DC × AC

Question : In the given trapezium ABCD, AB||CD and AB = 2CD. If area of ΔAOB = 84 cm², then the area of ΔCOD is
(a) 22 sq.cm 
(b) 25 sq.cm
(c) 21 sq.cm
(d) 24 sq.cm

Question : If a tree casts a 18 feet shadow and at the same time, a child of height 3 feet casts a 2 feet shadow, then the height of the tree is
(a) 27 feet
(b) 32 feet
(c) 45 feet
(d) 36 feet

Question : Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, then the distance between their tops is
(a) 13 m
(b) 12 m
(c) 14 m
(d) 15 m

Question : A 12 cm rod is held between a flashlight and a wall as shown. Find the length of the shadow on the wall if the rod is 45 cm from the wall and 15 cm from the light.
(a) 75 cm
(b) 96 cm
(c) 48 cm
(d) 60 cm

Question : An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1/2X1 hours?
(a) 300 √67 km
(b) 400 √61 km
(c) 200 √61 km
(d) 300 √61 km

Question : Mason Construction wants to connect two parks on opposite sides of town with a road. Surveyors have laid out a map as shown. The road can be built through the town or around town through point R. The roads intersect at a right angle at point R. The line joining Park A to Park B is parallel to the line joining C and D.

(a) What is the distance between the parks through town?
(b) What is the distance from Park A to Park B through point R?
       (i)          (ii)
(a) 9 m         13 m
(b) 8 m         12.5 m
(c) 8.75 m    12 m
(d) 9 m        14 m

Question : In rhombus ABCD, AB² + BC² + CD² + DA² =
(a) OA² + OB² 
(b) OB² + OC²
(c) OC² + OD²
(d) AC² + BD²

Question : In the given figure, ∠BAC = ∠ADC, then CA/CB is
(a) CB × CD
(b) CA²
(c) DC/AC
(d) CD²

Question : P and Q are points on sides AB and AC respectively of DABC. If AP = 3 cm, PB = 6 cm, AQ = 5 cm and QC = 10 cm, then BC =
(a) PQ
(b) 2PQ
(c) 3PQ
(d) 4PQ

Question : In the given figure, AD ⊥ BC, BE ⊥ AC, CF ⊥ AB, then AF² + BD² + CE² = 
(a) OA² + OB² + OC²
(b) OD² + OE² + OF²
(c) AB² + BC² + AC²
(d) AE² + BF² + CD²

Question :ABC is right triangle, right angled at C. If p is the length of the perpendicular from C to AB and a, b, c have the usual meaning, then 1/a² + 1/b²

(A) 1/p²
(b) 2/p²
(c) p²
(d) 2p²

Question : In the given ΔABC, AD ⊥ BC and ∠A is right angled. Then AD² =

(A) AB × AC
(b) BD × CD
(c) BC × AC
(d) AB × BC

Question : ΔABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ΔDEF ~ ΔABC and EF = 4 cm, then perimeter of ΔDEF is
(a) 7.5 cm
(b) 15 cm
(c) 22.5 cm
(d) 30 cm

Question : In the given figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, then CD =
(a) 16 cm 
(b) 14 cm
(c) 15 cm
(d) 17 cm

Question : In the given figure, ABC is a right triangle right-angled at B. AD and CE are the two medians drawn from A and C respectively. If AC = 5 cm and AD = 3 √5 / 2 cm, then the length of CE is
(a) 4 cm A
(b) 2 5cm
(c) 3 5cm
(d) 5 cm

Question : Match the following

(A) (P)→(1), (Q)→(2), (R)→(3), (S)→(4)
(b) (P)→(2), (Q)→(1), (R)→(3), (S)→(4)
(c) (P)→(4), (Q)→(2), (R)→(1), (S)→(3)
(d) (P)→(3), (Q)→(1), (R)→(4), (S)→(2)

Question : Which of the following statements is CORRECT?
(a) The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
(b) If a line is drawn parallel to one side of the triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
(c) All similar figures are congruent.
(d) If in two triangles, two angles of one triangle is equal to the two angles of the other triangle then two triangles may or may not be congruent.

Question :P and Q are the mid-points of the sides CA and CB respectively of a ΔABC, right angled at C, then find :
(i) 4AC² + BC²
(b) 4BC² + AC²
(c) 4(AQ² + BP²)
        (i)     (ii)    (iii)
(a) 4AQ² 4BP² 5AB²
(b) 5AQ² 5BP² 4AB²
(c) 4AQ² 5BP² 5AB²
(d) 5AQ² 4BP² 4AB²

Question : In the given figure, the line segment XY is parallel to side AC of ΔABC and it divides the triangle into two parts of equal area. Then, find

(i) AX : AB (ii) AC/XY(i)                      (ii)
(A) (2 + √2): 2 √2 − 2
(b) (2 − √2): 2 √2 −1
(c) (2 − √3): 3 3
(d) (2 + √2): 3 √2 − 3