Practice the AP 9th Class Maths Bits with Answers Chapter 7 Triangles on a regular basis so that you can attempt exams with utmost confidence.
AP State Syllabus 9th Class Maths Bits 7th Lesson Triangles with Answers
Choose the correct answer :
Question 1.
Figures having same shape and size are called …………… figures.
A) congruent
B) identical
C) similar
D) different
Answer:
A) congruent
Question 2.
Two squares are congruent if they have same
A) shape
B) side
C) angles
D) none
Answer:
B) side
Question 3.
If ∆PQR = ∆ABC then ∠R =
A) ∠A
B) ∠B
C) ∠C
D) right angle
Answer:
C) ∠C
Question 4.
Any two circles are
A) similar
B) congruent
C) equal
D) not equal
Answer:
A) similar
Question 5.
In the figure ΔABC = ΔCDA by
A) S.A.S.
B) R.H.S.
C) A.S.A.
D) S.S.S. B
Answer:
D) S.S.S. B
Question 6.
In the figure PQ = RS; bisect at ‘O’ then ΔPOR ≅ ΔQOS by
A) A.S.A
B) S.S.S
C) A.A.S.
D) S.A.S.
Answer:
D) S.A.S.
Question 7.
APQR is an isosceles triangle and ‘S’ is the mid-point of \(\overline{\mathrm{QR}}\), then ∆PQS =
A) ∆PSR
B) ∆RSP
C) ∆SPR
D) ∆PRS
Answer:
D) ∆PRS
Question 8.
\(\overline{\mathrm{XY}}\) is the perpendicular bisector of \(\overline{\mathrm{PQ}}\). Then ∆POX = ∆QOX by
A) S.A.S
B) A.S.A
C) S.S.S
D) A.A.A.
Answer:
A) S.A.S
Question 9.
If in ∆DEF; DF is the longest side then the greatest angle is
A) ∠D
B) ∠E
C) ∠F
D) right angle
Answer:
B) ∠E
Question 10.
If in ∆PQR, PQ > QR then
A) ∠R < ∠P
B) ∠P > ZQ
C) ∠R > ∠P
D) ∠P < ∠Q
Answer:
C) ∠R > ∠P
Question 11.
In ∆ABC, which of the following is true ?
A) AB + BC < AC
B) AB – AC > AC
C) BC + CA < AB
D) AB + BC > AC
Answer:
D) AB + BC > AC
Question 12.
In ∆XYZ, W is a point on YZ such that XW = XZ then
A) XY = XW
B) XY > XW
C) XY < XW
D) XY < XZ
Answer:
B) XY > XW
Question 13.
In the figure AB is a line segment and PQ is an arc with centre A then
A) ∠QAB < ∠PAB
B) ∠QAB < ∠PAB
C) ∠QAB = ∠PAB
D) None
Answer:
A) ∠QAB < ∠PAB
Question 14.
In the figure PA = PB and QA = QB then ∠POA is angle.
A) Acute
B) obtuse
C) right
D) reflex
Answer:
C) right
Question 15.
In rhombus ABCD, ∆AOB ≅
A) ∆BOC
B) ∆COD
C) ∆DOA
D) All of the above
Answer:
D) All of the above
Question 16.
In the figure PQ = SQ; PR = SR then ∆PQR ≅ ∆SQR by …………. congruence.
A) R.H.S.
B) S.A.S.
C) S.S.S.
D) A.S.A.
Answer:
C) S.S.S.
Question 17.
In ∆ABC, altitudes BD and CE are equal then ∆DCB ≅ ∆EBC by ………….. congruence
A) A.S.A.
B) S.A.S.
C) S.S.S.
D) R.H.S.
Answer:
D) R.H.S.
Question 18.
In ∆PQR, PQ = PR and RT and QU are medians then ∆QRT = ∆RQU by congruence.
A) R.H.S.
B) S.A.S.
C) A.S.A.
D) S.S.S.
Answer:
B) S.A.S.
Question 19.
∆ABC is isosceles with sides AB = AC; AD is the altitude, if ∠BAD = 50° then ∠CAD =
A) 40°
B) 130°
C) 50°
D) None
Answer:
C) 50°
Question 20.
If three angles of a triangle are equal to three angles of anothertriangle then they are
A) congruent
B) equal
C) similar
D) can’t be said
Answer:
A) congruent
Question 21.
From the given figures, we observe that
A) ∆ DEF ≈ ∆ ABC
B) ∆ EDF ≈ ∆ ABC
C) ∆ FDE ≈ ∆ ABC
D) None of the above
Answer:
C) ∆ FDE ≈ ∆ ABC
Question 22.
In the given figure AB and CD are in-tersecting at ‘O’. OA = OB, OP = OC, then
A) AD = BC
B) AD // BC
C) AB = CD
D) ∆ AOD ≈ ∆ COB
Answer:
B) AD // BC
Question 23.
In the given figure, AB // DC and AD // BC, then
A) ∆ ABC ≅ ∆ CDA
B) ∆ ABC ≅ ∆ DAC
C) ∆ ABC ≅ ∆ ADC
D) ∆ ABC ≅ ∆ ACD
Answer:
A) ∆ ABC ≅ ∆ CDA
Question 24.
In ∆ ABC, ∠BAD = ∠CAD and BD = DC, then
A) ∆ ABC is equilateral
B) ∆ ABC is scalene
C) ∆ ABC is isosceles
D) ∆ ABC is right angled
Answer:
C) A ABC is isosceles
Question 25.
The angle of an equilateral triangle is
A) 30°
B) 45°
C) 90°
D) 60°
Answer:
D) 60°
Question 26.
In ∆ ABC, AB = AC and AP ⊥ BC, we can prove that ∠B = ∠C using
A) SSS congruency rule
B) RHS congruency rule
C) SAS congruency rule
D) ASA congruency rule B
Answer:
B) RHS congruency rule
Question 27.
In AABC, AB > AC, then
A) ∠C < ∠B
B) AB + AC < BC
C) ∠C > ∠B
D) AB – AC > BC
Answer:
C) ∠C > ∠B
Question 28.
Which of the following set of measure-ments is not possible to construct a triangle ?
A) 5 cm, 8 cm, 4 cm
B) 5 cm, 4 cm, 3 cm
C) 7 cm, 5 cm, 3 cm
D) 5 cm, 8 cm, 1 cm
Answer:
D) 5 cm, 8 cm, 1 cm
Question 29.
Which measurement is required to make a triangle along with sides 4 cm and 6 cm ?
A) 1 cm
B) 2 cm
C) 3 cm
D) 1.5 cm
Answer:
C) 3 cm
Question 30.
Which of the following statement is not correct ?
A) In ΔABC, ∠A + ∠B + ∠C = 180°
B) In ΔABC, if AB > BC, then C > A
C) In a right angled triangle, the hypot-enuse is the smallest side
D) In ΔABC, if AB = BC, then ∠C = ∠B
Answer:
C) In a right angled triangle, the hypot-enuse is the smallest side
Question 31.
Which congruency rule is applied in the following figures ?
A) R.H.S.
B) A.S.A.
C) SAS.
D) S.S.S
Answer:
C) SAS.
Question 32.
Which congruency rule is apt for the following figures ?
A) S.S.S.
B) S.A.S.
C) A.S.A.
D) R.H.S.
Answer:
A) S.S.S.
Question 33.
Which congruency rule is followed in the following figures ?
A) S.A.S.
B) A.S.A.
C) R.H.S.
D) S.S.S.
Answer:
B) A.S.A.
Question 34.
Which congruency rule is taken into consideration in the following figures ?
A) S.S.S
B) S.A.S
C) A.S.A
D) R.H.S
Answer:
D) R.H.S
Question 35.
In ΔPQR, PQ = 5 cm, QR = 12 cm and PR = 13 cm, then PQR is
A) an acute angled triangle
B) a right angled triangle
C) an obtuse angled triangle
D) an equilateral triangle
Answer:
B) a right angled triangle
Question 1.
Among the following a true statement in ΔABC is
A) \(\overline{\mathrm{AB}}+\overline{\mathrm{BC}}<\overline{\mathrm{AC}}\)
B) \(\overline{\mathrm{BC}}+\overline{\mathrm{CA}}<\overline{\mathrm{AB}}\) C) \(\overline{\mathrm{AC}}+\overline{\mathrm{AB}}>\overline{\mathrm{BC}}\)
D) \(\overline{\mathrm{AB}}+\overline{\mathrm{BC}}=\overline{\mathrm{AC}}\)
Answer:
C) \(\overline{\mathrm{AC}}+\overline{\mathrm{AB}}>\overline{\mathrm{BC}}\)
Question 2.
In ΔABC, AB = 8 cm, BC = 5 cm, CA = 9 cm then the greatest angle is
A) ∠A
B) ∠B
C) ∠C
D) ∠B, ∠C
Answer:
B) ∠B
Question 3.
In ΔABC, BC = 10 cm, CA = 15 cm then the measure of AB is
A) Less than 25 cm
B) Greater than 25 cm
C) Equal to 25 cm
D) Less than 5 cm
Answer:
B) Greater than 25 cm
Question 4.
In which figure represents Δ ABC ≅ Δ XYZ w.r.t. to the A.S.A. rule ?
Answer:
C
Question 5.
In ΔXYZ, if ∠X = 40°, ∠Y = 60°, ∠Z = 80° then the smallest side is …………….
A) \(\overline{X Y}\)
B) \(\overline{Y Z}\)
C) \(\overline{Y Z}\)
D) both B and C
Answer:
B) \(\overline{Y Z}\)
Question 6.
In Δ ABC, AB = AC and an exterior angle ∠ACD = 105° then ∠BAC – ?
A) 105°
B) 60°
C) 30°
D) 75°
Answer:
C) 30°
Question 7.
In a Δ ABC, AD and BE are medians of Δ ABC and BE || DF, then the ratio of CF : AC
A) 1 : 3
B) 3 : 1
C) 4 : 1
D) 1 : 4
Answer:
D) 1 : 4
Question 8.
In Two right angle triangles their hy-potenuse AB, EF are equal and AC = DE then which is true statement of the following ?
A) ΔABC ≅ ΔDEF
B) ΔABC ≅ ΔEFD
C) ΔACB ≅ ΔEDF
D) Both B and C
Answer:
D) Both B and C
Question 9.
Three angles of a Triangle are in the ratio 2:3:5 then the angles are
A) 30°, 60°, 90°
B) 36°, 54°, 90°
C) 40°, 50°, 90°
D) 40°, 60°, 80°
Answer:
B) 36°, 54°, 90°
Question 10.
The angles of a triangle are in the ra-tio 5 : 3 : 7 then, the triangle is
A) An obtuse angled triangle
B) Right angle triangle
C) An Isosceles triangle
D) An acute angled triangle
Answer:
D) An acute angled triangle
Question 11.
From the adjacent figure, the value of x + y is
A) 110°
B) 140°
C) 170°
D) 30°
Answer:
A) 110°
Question 12.
In ΔABC, ∠A = 40°. If \(\overrightarrow{\mathbf{B O}}\) and \(\overrightarrow{\mathbf{C O}}\) are the bisectors of ZB and ZC, then the value of ∠BOC is
A) 110°
B) 70°
C) 40°
D) 140°
Answer:
A) 110°
Question 13.
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
A) An isosceles triangle
B) An obtuse triangle
C) An equilateral triangle
D) A right triangle
Answer:
C) An equilateral triangle
Question 14.
The ratio of angles in a triangle is 1:2:3 then the triangle is
A) Equilateral
B) Isosceles
C) Obtuse angled
D) Right angled
Answer:
D) Right angled
Question 15.
Which is not Pythagorean triplet in the following
A) (3, 4, 5)
B) (1, 2, 3)
C) (6, 8, 10)
D) (5, 12, 13)
Answer:
B) (1, 2, 3)
Question 16.
From the given figure area of ΔABC is
A) \(\frac { 1 }{ 2 }\) x AC x BC
B) \(\frac { 1 }{ 2 }\) x AB x BC
C) \(\frac { 1 }{ 2 }\) x AB x AC
D) \(\frac { 1 }{ 2 }\) x AB x BC x AC
Answer:
C) \(\frac { 1 }{ 2 }\) x AB x AC
Question 17.
Which of these is a postulate ?
A) A.A.A.
B) A.S.A.
C) S.S.S.
D) S.A.S.
Answer:
A) A.A.A.
Question 18.
In the given diagram BD = AD and AC = CD, then ∠CAB : ∠ABD
A) 3 : 1
B) 1 : 3
C) 1 : 4
D) 4 : 1
Answer:
A) 3 : 1
Question 19.
In ΔABC, D, E are the mid points of \(\overline{\mathbf{A}} \overline{\mathbf{B}}, \overline{\mathbf{A C}}\) . F, G are the mid-points of \(\overline{\mathrm{AD}}, \overline{\mathrm{AE}}\) . If \(\overline{\mathbf{F G}}\) = 2 cm, then BC =
A) 10 cm
B) 4 cm
C) 6 cm
D) 8 cm
Answer:
D) 8 cm
Question 20.
ΔPQR is an equilateral triangle. X, Y, Z are the mid-points of the sides and A, B, C are the mid-points of sides of ΔXYZ. If the perimeter of ΔPQR is 8.4 cm, then the perimeter of ΔABC =
A) 4.2 cm
B) 8.4 cm
C) 2.1 cm
D) 2.8 cm
Answer:
D) 2.8 cm
Read the given data and answer the questions form 21 to 25.
Question 21.
From the data given, in APQR, PQ + PR = …………….cm.
A) 25
B) 19
C) 9.4
D) 10.4
Answer:
D) 10.4
Question 22.
The exterior angle at R in ΔPQR is
A) 120°
B) 60°
C) 80°
D) 100°
Answer:
C) 80°
Question 23.
Which are congruent in the given tri-angles?
A) None of these
B) ΔABC ≅ ΔXYZ
C) ΔXYZ ≅ ΔPQR
D) ΔABC ≅ ΔPQR
Answer:
D) ΔABC ≅ ΔPQR
Question 24.
In ΔXYZ the biggest angle is at which vertex ?
A) X + Y + Z
B) X
C) Y
D) Z
Answer:
B) X
Question 25.
ΔABC ≅ ΔPQR under which congru-ency criterion ?
A) A. A. A
B) S. S. S
C) S. A. S
D) A. S. A
Answer:
A) A. A. A
Question 26.
In the given triangle is it possible to exist all exterior angles as right angles.
A) Never possible
B) Always possible
C) Sometimes possible
D) There can be 2 rights angles
Answer:
D) There can be 2 rights angles
Question 27.
“In a triangle median divides the tri-angle into two triangles whose areas are equal.” Rough diagram for the above statement is
Answer:
B
Question 28.
From the given figure, what is the additional information needed to prove ΔOBE ≅ ΔOCD ?
A) BE = CD
B) ΔBOE = ΔCOD
C) ΔOBE = ΔOCD
D) BD = CE
Answer:
B) ΔBOE = ΔCOD
Question 29.
□ABCD is a Rhombus prove that the diagonals divide the rhombus into four congruent triangles, (let the point of intersection is O.) For the above problem what is R.T.P. ?
A) ΔABC ≅ ΔACD ≅ ΔABD ≅ ΔBCD
B) ΔABC ≅ ΔACD
C) ΔABD ≅ ΔBCD
D) ΔOAB ≅ ΔOBC ≅ ΔOCD ≅ ΔOAD
Answer:
D) AOAB ≅ AOBC ≅ AOCD ≅ AOAD
Question 30.
From the given figure, what is the ad-ditional information needed to prove ΔOBE ≅ ΔOCD ?
A) BE = CD
B) ∠BOE = ∠COD
C) ∠OBE = ∠OCD
D) BD = CE
Answer:
D) BD = CE
Question 31.
In ΔABC, \(\overline{\mathrm{AD}}, \overline{\mathrm{BE}}\) are medians \(\overline{\mathrm{BE}} \| \overline{\mathrm{DF}}\)
To prove CF = \(\frac { 1 }{ 4 }\) AC it was written as
In ΔABC ‘D’ is the mid-point of \(\overline{\mathrm{BC}}\) and BE || DF. As per triangle mid-point of \(\overline{\mathrm{CE}}\) .
CF = \(\frac { 1 }{ 2 }\) CE
Which of the following is the next step ?
A) CF = \(\frac { 1 }{ 2 }\)AC
B) 2CF = CE
C) CF = \(\frac { 1 }{ 2 }\) (\(\frac { 1 }{ 2 }\) AC)
D) 4CF = AC
Answer:
B) 2CF = CE
Question 32.
In ΔABC, ∠B = ∠C and if AB = x – 8, AC = 2x – 53, then x =
A) 45 units
B) 37 units
C) 29 units
D) 25 units
Answer:
A) 45 units
Question 33.
In triangle ABC, D is the mid-point of \(\overline{\mathrm{BC}}\) and \(\overline{\mathbf{A}} \overline{\mathbf{B}}=\overline{\mathbf{A C}}\) . If A and D are joined ΔABD ≅ ΔACD under the congruency rule.
A) A.S.A
B) S.A.S
C) A.A.A
D) S.S.S
Answer:
B) S.A.S
Question 34.
The circle which passes through all the three vertices of a triangle is
A) Incircle
B) Orthocircle
C) Circumcircle
D) Outercircle
Answer:
C) Circumcircle
Question 35.
The exterior angle of an equilateral triangle is
A) 30°
B) 60°
C) 90°
D) 120°
Answer:
D) 120°
Question 36.
Which one is not a congruency axiom of triangle ?
A) S.S.S.
B) S.A.S.
C) A.S.A
D) A.A.A
Answer:
D) A.A.A
Question 37.
Which congruency property is related to satisfy ΔABC ≅ ΔABD in the given figure
A) S. A. S
B) A.S.A
C) S.S.S
D) R.H.S
Answer:
A) S. A. S
Question 38.
The area of triangle of base 8 cm is 20 sq.cm then, length of the altitude of the triangle is ………..
A) \(\frac { 5 }{ 2 }\) cm
B) 5 cm
C) 80 cm
D) 160 cm
Answer:
B) 5 cm
Question 39.
If a, b and c are the lengths of sides of a triangle, which of the following is TRUE?
A) a + b>c, a-b>c
B) a + b < c, a-bc, a-b<c
D) a + b < c, a – b > c
Answer:
C) a + b>c, a-b ∠A > ∠C
C) ∠A < ∠B < ∠C
D) ∠B < ∠A < ∠C Answer: B) ∠B > ∠A > ∠C
Question 40.
If AB = QR, BC = PR and CA = PQ, then
A) ΔABC ≅ ΔPQR
B) ΔCBA ≅ ΔPRQ
C) ΔBAC ≅ ΔRPQ
D) ΔPQR ≅ ΔBCA
Answer:
B) ΔCBA ≅ ΔPRQ
Question 41.
What is the number of triangles that can be constructed with all positive integer sides if two sides are 3 cm, 3cm?
A) 3
B) 5
C) 6
D) 9
Answer:
B) 5
Question 42.
Number of independent measure-ments required to construct a triangle
A) 3
B) 2
C) 1
D) 0
Answer:
A) 3
Question 43.
Which of the following triangle con-gruency criteria is used to prove ΔABD ≅ ΔACD ?
A) SSS Congruency
B) SAS Congruency
C) ASA Congruency
D) RHS Congruency
Answer:
B) SAS Congruency
Question 44.
In triangle ABC, AB = 5 cm, BC = 4 cm, CA = 3 cm, which of the following is TRUE?
A) ∠A = ∠B = ∠C
B) ∠B > ∠A > ∠C
C) ∠A < ∠B < ∠C
D) ∠B < ∠A < ∠C Answer: B) ∠B > ∠A > ∠C
Question 45.
In a right triangle ABC, AB = AC, then which of the following is FALSE ?
A) (∠B + ∠C) > ∠A
B) ∠A > ∠B, ∠A > ZC
C) ∠A = ∠B + ∠C
D) ∠A = 2∠B = 2∠C
Answer:
C) ∠A = ∠B + ∠C