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question_answer1)
In \[\Delta ABC,\] \[AB=AC\] and AD is perpendicular to BC. State the property by which \[\Delta ADB=\Delta ADC\].
A)
S.A.S. property done
clear
B)
S.S.S. property done
clear
C)
R.H.S. property done
clear
D)
A.S.A, property done
clear
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question_answer2)
Two students drew a line segment each. What is the condition for them to be congruent?
A)
They should be drawn with a scale. done
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B)
They should be drawn on the same sheet of paper. done
clear
C)
They should have different lengths. done
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D)
They should have the same length. done
clear
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question_answer3)
In the given figure, if \[AD=BC\] and \[AD||BC,\]which of the following is true?
A)
\[AB=AD\] done
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B)
\[AB=DC\] done
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C)
\[BC=CD\] done
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D)
\[AC=AD\] done
clear
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question_answer4)
In \[\Delta PQR\] and \[\Delta XYZ,\] \[\angle P={{50}^{o}},\] \[XY=PQ\], and \[XZ=PR\]. By which property are \[\Delta XYZ\] and \[\Delta PQR\] congruent?
A)
S.S.S. property done
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B)
S.A.S. property done
clear
C)
A.S.A. property done
clear
D)
R.H.S. property done
clear
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question_answer5)
A: Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other. |
R: Two triangles are congruent if two sides and the included angle of one are equal to the corresponding two sides and included angle of the other. |
Given A & R, which of the following statements is correct?
A)
A is false and R is the correct explanation of A. done
clear
B)
A is true and R is the correct explanation of A. done
clear
C)
A is true and R is false. done
clear
D)
A is false and R is true. done
clear
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question_answer6)
Two triangles, A PQR and ADEF are of the same size and shape. What can we conclude about them?
A)
\[\Delta PQR\] is smaller than \[\Delta DFE\]. done
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B)
\[\Delta PQR\] is larger than \[\Delta DFE\]. done
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C)
\[\Delta PQR\] is congruent to \[\Delta DFE\]. done
clear
D)
\[\Delta PQR\] is not congruent to \[\Delta DFE\]. done
clear
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question_answer7)
Which of the following examines the congruence of plane figures?
A)
Trial and error method done
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B)
Superposition method done
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C)
Substitution method done
clear
D)
Transposition method done
clear
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question_answer8)
Which of the following is a pair of congruent figures?
A)
A regular pentagon and a regular hexagon. done
clear
B)
A rhombus and a square. done
clear
C)
Two equilateral triangles of the same length of their sides. done
clear
D)
A quadrilateral and a rectangle. done
clear
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question_answer9)
A In \[\Delta ABC\] and \[\Delta PQR,\] \[AB=x\text{ }cm,\] \[BC=y\text{ }cm\]and \[CA=z\text{ }cm\]. What are the measures of sides PQ, QR and RP of \[\Delta PQR\] if \[\Delta ABC\cong \Delta ABC\cong \Delta PQR\]?
A)
B)
C)
D)
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question_answer10)
Direction: In the given figure, \[AD=CD\] and \[AB=CB\].
What are the three pairs of equal parts?
A)
\[\angle ADB=\angle CDB,\angle ABD=\angle CBD;\,\,BD=BD\] done
clear
B)
\[AD=AB,\text{ }DC=CB,\text{ }BD=BD\] done
clear
C)
\[AB=CD,AD=BC,BD=BD\] done
clear
D)
\[\angle ADB=\angle CDB,\angle ABD=\angle CBD;\,\,\angle DAB=\angle DBC\] done
clear
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question_answer11)
Direction: In the given figure, \[AD=CD\] and \[AB=CB\].
Which of the following is the correct conclusion?
A)
\[\Delta ABC\] and \[\Delta \,CBD\] are isosceles triangles. done
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B)
BD bisects \[\angle ADC\] done
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C)
BD bisects \[\angle BAD\] done
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D)
\[\Delta ABC\] and \[\Delta CBD\] are equilateral triangles. done
clear
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question_answer12)
In the given figure, \[AB=AC\] and AD is the bisector of \[\angle BAC\].
Which among the following statements is true?
A)
\[\Delta ADB\cong \Delta ABC\] done
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B)
\[\Delta ADC\cong \Delta ABC\] done
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C)
\[\angle B=\angle C\] done
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D)
\[\angle ABC=\angle CAB\] done
clear
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question_answer13)
In \[\Delta ABC\] and \[\Delta DEF,\] \[AC=DF,AB=DE\] and \[BC=EF\]. By which property are \[\Delta ABC\] and \[\Delta DEF\] congruent?
A)
R.H.S. property done
clear
B)
S.S.S. property done
clear
C)
S.A.S. property done
clear
D)
A.S.A. property done
clear
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question_answer14)
For the triangles \[\Delta ART\] and \[\Delta PEN\]given, if S.A.S. criterion should be used given \[\angle T=\angle N\] what are the respective measures of PN and RT?
A)
TR and PE done
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B)
AR and PEA done
clear
C)
AT and EN done
clear
D)
AR and PN done
clear
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question_answer15)
Which of the following is an example of A.S.A. criterion of congruency for two triangles \[\angle ADB\] and \[\angle DEF\]?
A)
\[AB=EF,\text{ }\angle B=\angle E\] and \[\angle C=\angle F\] done
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B)
\[BC=EF,\text{ }\angle B=\angle E\] and \[\angle C=\angle F\] done
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C)
\[AC=EF,\text{ }\angle B=\angle D\] and \[\angle C=\angle F\] done
clear
D)
\[AC=DE,\text{ }\angle B=\angle D\] and \[\angle C=\angle F\] done
clear
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question_answer16)
In the figure given, \[AC=BD\] and \[\angle BAC=\angle CDB={{90}^{o}}\]
If \[\Delta ABC=\Delta DCB\] by R.H.S. property which of the following is required?
A)
The measure of AB. done
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B)
The measure of CD. done
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C)
The measure of BC. done
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D)
\[AC=BD\] done
clear
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question_answer17)
Which of the following criterion does not exist?
A)
A.S.A. criterion done
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B)
R.H.S. criterion done
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C)
A.A.A. criterion done
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D)
S.S.S. criterion done
clear
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question_answer18)
In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?
A)
One triangle is an enlarged copy of other. done
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B)
The two triangles are necessarily congruent. done
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C)
The two triangles are congruent by A.A.A. congruency criterion. done
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D)
All of the above. done
clear
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question_answer19)
Direction: \[\Delta ABC\] is congruent to \[\Delta PQR\] under the correspondence \[ABC\overset{{}}{\longleftrightarrow}RQP\]. |
Which part corresponds to PQ?
A)
\[\overline{CB}\] done
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B)
\[\overline{AC}\] done
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C)
\[\overline{QR}\] done
clear
D)
\[\overline{AB}\] done
clear
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question_answer20)
Direction: \[\Delta ABC\] is congruent to \[\Delta PQR\] under the correspondence \[ABC\overset{{}}{\longleftrightarrow}RQP\]. |
Which part of corresponds to RP?
A)
\[\overline{AB}\] done
clear
B)
\[\overline{AC}\] done
clear
C)
\[\overline{CA}\] done
clear
D)
\[\overline{BC}\] done
clear
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question_answer21)
\[\Delta ABC\] is congruent to \[\Delta XYZ\]. Find the measures of \[\angle x\] and \[\angle y\] respectively.
A)
\[{{80}^{o}},{{60}^{o}}\] done
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B)
\[{{60}^{o}},{{40}^{o}}\] done
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C)
\[{{80}^{o}},{{40}^{o}}\] done
clear
D)
\[{{60}^{o}},{{80}^{o}}\] done
clear
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question_answer22)
\[\Delta ABC\cong \Delta FDE\]and \[AB=3\text{ }cm,\] \[EF=8\text{ }cm\]and \[DF=10\text{ }cm\]. What are the respective lengths of AC and DE in cm?
A)
\[10,\,3\] done
clear
B)
\[10,\,8\] done
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C)
\[8,\,3\] done
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D)
\[3,\,10\] done
clear
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question_answer23)
\[\Delta ABC\cong \Delta FDE\] What is the measure of \[\angle F\]?
A)
\[{{70}^{o}}\] done
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B)
\[{{50}^{o}}\] done
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C)
\[{{130}^{o}}\] done
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D)
\[{{60}^{o}}\] done
clear
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question_answer24)
In the figure, \[PQ\text{ =}PS\] and \[QR=SR\]. If \[\Delta PQR\] is congruent to \[\Delta PSR,\] which of the following is correct?
A)
\[\angle QPR=\angle PRS\] done
clear
B)
\[\angle RPS=\angle RQP\] done
clear
C)
\[\angle QRP=\angle SRP\] done
clear
D)
\[\overline{PR}=\overline{RS}\] done
clear
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question_answer25)
AB and AC are two chords of a circle with centre O as shown.
If \[\Delta AOB\] is congruent to \[\Delta AOC,\] which of the following is correct?
A)
\[\angle OBA=\angle OCA\] done
clear
B)
\[\angle AOC=\angle OCA\] done
clear
C)
\[AO=AC\] done
clear
D)
\[AB=OC\] done
clear
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question_answer26)
A regular hexagon is divided into four triangles.
Which of the following is correct?
A)
\[\Delta ABF\cong \Delta EDF\] done
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B)
\[\Delta FDC\cong \Delta FCB\] done
clear
C)
\[\Delta ABF\cong \Delta FBC\] done
clear
D)
\[\Delta FDC\cong \Delta BCF\] done
clear
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question_answer27)
\[\Delta ABC\] and \[\Delta DEF\] are as shown.
By which condition of congruence is\[\Delta ABC\cong \Delta DEF\]?
A)
S.S.S. condition done
clear
B)
S.A.S. condition done
clear
C)
R.H.S. condition done
clear
D)
A.S.A. condition. done
clear
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question_answer28)
Given \[AB||CD\] and AB = CD, which of the following is correct?
A)
\[\Delta AOB\cong \Delta DOC\] done
clear
B)
\[\Delta AOB\cong \Delta ODC\] done
clear
C)
\[\Delta BOA\cong \Delta DOC\] done
clear
D)
\[\Delta BAO\cong \Delta COD\] done
clear
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question_answer29)
\[\Delta ABC\] is isosceles, \[AB=AC\] and \[AD\bot BC,\]
Which of the following is correct?
A)
\[\Delta ADC\cong \Delta ADB\] done
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B)
\[\Delta ADB\cancel{\cong }\Delta ADB\] done
clear
C)
\[\Delta ADB\cong \Delta ABC\] done
clear
D)
\[\Delta ABC\cong \Delta ADC\] done
clear
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question_answer30)
Observe the triangles given in the figure.
State the condition under which \[\Delta ABC\cong \Delta PQR\]
A)
A.S.A. done
clear
B)
S.S.S. done
clear
C)
S.A.S. done
clear
D)
R.H.S. done
clear
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question_answer31)
In the given figure, \[AB=AC\] and \[AD=AE\].
Which of the following statements is not true?
A)
\[\angle CAE=\angle BAD\] done
clear
B)
\[\Delta ACE=\Delta ABD\] done
clear
C)
\[\Delta AEC=\Delta ABD\] done
clear
D)
\[BE=DC\] done
clear
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question_answer32)
ABCD is a parallelogram in which \[AB=DC\] and \[AD=BC\].
By which condition of congruence of triangles is\[\Delta ABD\cong \Delta CDB\]?
A)
R.H.S. done
clear
B)
S.A.S. done
clear
C)
S.S.S. done
clear
D)
A.S.A. done
clear
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question_answer33)
Given \[\Delta XYZ\] and \[\Delta LMN.\]
Choose the correct statement.
A)
\[\Delta XYZ\cong \Delta LMN\] done
clear
B)
\[YZ=LM\] done
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C)
\[XY=MN\] done
clear
D)
\[XZ=LM\] done
clear
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question_answer34)
Identify the incorrect statement.
A)
The corresponding sides of congruent triangles are equal. done
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B)
The corresponding angles of congruent triangles are equal. done
clear
C)
Two triangles cannot be congruent. done
clear
D)
There are four congruency conditions for congruence of triangles. done
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question_answer35)
A By which congruency property are the two triangles PQS and PRS given in the following figure congruent?
A)
S.S.S. property done
clear
B)
S.A.S. property done
clear
C)
A.S.A. property done
clear
D)
R.H.S. property done
clear
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question_answer36)
In the following figure, two triangles ABC and EDC are such that \[AC=EC,\text{ }BC=DC,\] \[\angle E={{60}^{o}},\] \[\angle DCE={{30}^{o}},\] and \[\angle B={{90}^{o}},\]. By which property is \[\Delta ABC\cong \Delta EDC\]?
A)
S.S.S. property done
clear
B)
S.A.S. property done
clear
C)
A.S.A. property done
clear
D)
R.H.S. property done
clear
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question_answer37)
For the congruence of \[\Delta ABC\] and \[\Delta PQR,\] which one of the following sets of conditions is not sufficient?
A)
\[\angle ABC=\angle PQR,\] \[a=p,\,\,c=r\] done
clear
B)
\[\angle CAB=\angle RPQ,\angle ABC=\angle PQR,c=r\] done
clear
C)
\[b=q,\,\,\angle CAB=\angle RPQ,\,\,a=p\] done
clear
D)
\[a=p,\,c=r,\,\angle ABC=\angle PQR\] done
clear
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question_answer38)
Which of the following are congruent?
A)
Two Rs. 1 coins done
clear
B)
A Rs. 1 coin and a Rs. 2 coin done
clear
C)
A Rs. 2 coin and a Rs. 5 coin done
clear
D)
A Rs. 5 coin and a Rs. 10 coin done
clear
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question_answer39)
Which of the following is important in congruence of triangles?
A)
Naming the angles of the triangles using capital letters. done
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B)
Measures of angles in degrees. done
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C)
The order of letters of the triangles. done
clear
D)
Exact length of the sides of the triangles. done
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question_answer40)
In the figure given, which of the following statements is true?
A)
\[\Delta QPR\cong \Delta SPR\] done
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B)
\[\Delta PSR\cong \Delta RQP\] done
clear
C)
\[\Delta PRS\cong \Delta QPR\] done
clear
D)
\[\Delta QRP\cong \Delta PSR\] done
clear
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question_answer41)
In two triangles, pairs of corresponding sides and the corres-ponding angles are equal. What can be concluded from this?
A)
The triangles are small. done
clear
B)
The triangles are congruent. done
clear
C)
The triangles are equilateral. done
clear
D)
The triangles are equiangular. done
clear
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question_answer42)
Which of the following are measurements of two triangles by which they are congruent under S.A.S condition?
A)
\[\Delta ABC:\angle B={{50}^{o}},BC=5cm,\] and \[AB=7cm.\] \[\Delta DEF:\angle E={{50}^{0}},EF=7cm,\]and\[DE=5cm.\] done
clear
B)
\[\Delta ABC:BC=6cm,\] \[AC=4\,\,cm\] and \[\angle B={{35}^{o}}\] \[\Delta DEF:DF=4\,cm,\] \[EF=6\,cm\] and \[\angle D={{55}^{o}}\] done
clear
C)
\[\Delta ABC:AB=4.5cm,\]\[AC=4cm\]and\[\angle A={{60}^{o}}\] \[\Delta DEF:DE=4cm,FD=4.5cm\]and\[\angle D={{55}^{o}}\] done
clear
D)
Either [b] or [c] done
clear
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question_answer43)
\[\Delta ABC\] is isosceles with \[AB=AC,\] \[AD\bot BC;\] which of the following is a correct statement?
A)
\[\Delta ABC\cong \Delta ADC\] done
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B)
\[\Delta ABD\cong \Delta ACD\] done
clear
C)
\[\Delta ADB\cong \Delta ACD\] done
clear
D)
\[\Delta ADC\cong \Delta ABD\] done
clear
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question_answer44)
Are triangles in the given figure congruent by R.H.S. condition?
A)
Yes done
clear
B)
Insufficient data done
clear
C)
No done
clear
D)
Either [b] or [c] done
clear
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