MCQOPTIONS
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MCQOPTIONS
This section includes 33 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
\[\Delta BDC\cong \Delta MLK.\] Which of the following is correct? |
| A. | \[DB=MK;\,\angle D=\angle M,\angle C=LK\] |
| B. | \[BC=MK;\,\angle D=\angle L,DC=LK\] |
| C. | |
| D. | \[DB=MK;DC=\angle K;\angle B=ML\] |
| Answer» C. | |
| 2. |
How many triangles are congruent to A ABE in the given figure? |
| A. | 8 |
| B. | 9 |
| C. | |
| D. | 16 |
| Answer» E. | |
| 3. |
Consider the following statements. (i)If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent. (ii) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent. Of these two statements, which of the following is correct? |
| A. | (i) is true and (ii) is false. |
| B. | Both (i) and (ii) are false. |
| C. | |
| D. | (i) is false and (ii) is true. |
| Answer» B. Both (i) and (ii) are false. | |
| 4. |
In the adjacent figure, C is the mid point of AB, \[\angle CAD=\angle CBE\]and \[\angle ACE=\angle BCD.\] By which congruency condition\[\Delta DAC\cong \Delta EBC?\] |
| A. | R.H.S. |
| B. | S.S.S. |
| C. | PRS |
| D. | A.S.A. |
| Answer» D. A.S.A. | |
| 5. |
Vani wants to prove that \[\Delta FGH\cong \Delta JKL\]using R.H.S. congruency rule. She knows that FG = JK and FH = JL. What additional piece of information does she need? |
| A. | \[\angle H=\angle K={{90}^{o}}\] |
| B. | \[\angle F=\angle G={{90}^{o}}\] |
| C. | QRT |
| D. | \[\angle F=\angle J={{90}^{o}}\] |
| Answer» C. QRT | |
| 6. |
Consider the following statements. (i) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent. (ii) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangles congruent. (iii) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent. Which of the statement are correct? |
| A. | (i), (ii) and (iii) are correct |
| B. | (i) and (ii) are correct |
| C. | PSQ |
| D. | (ii) and (iii) |
| Answer» B. (i) and (ii) are correct | |
| 7. |
If \[\Delta ABC\cong \Delta PRQ,\] then \[\angle B\] and PQ are respectively equal to |
| A. | \[\angle P\] and AC |
| B. | \[\angle P\] and BC |
| C. | \[\angle R\] and AC |
| D. | \[\angle Q\] and AB |
| Answer» D. \[\angle Q\] and AB | |
| 8. |
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. | PQ QR RP x cm y cm z cm |
| B. | PQ QR RP y cm x cm z cm |
| C. | PQ QR RP x cm z cm y cm |
| D. | PQ QR RP z cm x cm y cm |
| Answer» B. PQ QR RP y cm x cm z cm | |
| 9. |
\[\Delta ABC\] is isosceles with \[AB=AC,\] \[AD\bot BC;\] which of the following is a correct statement? |
| A. | \[\Delta ABC\cong \Delta ADC\] |
| B. | \[\Delta ABD\cong \Delta ACD\] |
| C. | \[\Delta ADB\cong \Delta ACD\] |
| D. | \[\Delta ADC\cong \Delta ABD\] |
| Answer» C. \[\Delta ADB\cong \Delta ACD\] | |
| 10. |
In the given figure, \[\Delta \,ABC\] is congruent to \[\Delta \,PQR\]. What is the value of \[(m+2n+3p)\] |
| A. | 8 |
| B. | 10 |
| C. | 17 |
| D. | 19 |
| Answer» E. | |
| 11. |
In the given figure \[PQ||RS\] What is the value of \[(PR+QS)\]? |
| A. | \[21\,cm\] |
| B. | \[28\,cm\] |
| C. | \[25\,cm\] |
| D. | \[31\,cm\] |
| Answer» D. \[31\,cm\] | |
| 12. |
The given figure shows \[\Delta ABC\] & \[\Delta DBC,\] \[AB=DB\]and \[CA=CD\] What is the measure of \[\angle DBC\]? |
| A. | \[115{}^\circ \] |
| B. | \[100{}^\circ \] |
| C. | \[150{}^\circ \] |
| D. | \[155{}^\circ \] |
| Answer» B. \[100{}^\circ \] | |
| 13. |
In the given figure of a hockey field, \[\Delta ABC\] is congruent to \[\Delta PQR\]. If \[PC=200\text{ }cm,\]and \[AP=CR\] then what is the length of AR? |
| A. | 150 metres |
| B. | 300 metres |
| C. | 470 metres |
| D. | 500 metres |
| Answer» C. 470 metres | |
| 14. |
In the given figure (not to scale) \[AB=CD\] and \[BC=DE\] What type of a triangle is \[\Delta ACE\]? |
| A. | Isosceles triangle |
| B. | Equilateral triangle |
| C. | Scalene right - angled triangle |
| D. | Right - angled isosceles triangle |
| Answer» C. Scalene right - angled triangle | |
| 15. |
In the given figure of a field, PQR and RST are right- angled at Q and S respectively. The measure of the sides are given (See figure) What type of a triangle is \[\Delta PRT\]? |
| A. | Isosceles triangle |
| B. | Equilateral triangle |
| C. | Scalene right - angled triangle |
| D. | Right - angled isosceles triangle. |
| Answer» E. | |
| 16. |
Which of the following are congruent? |
| A. | Two Rs. 1 coins |
| B. | A Rs. 1 coin and a Rs. 2 coin |
| C. | A Rs. 2 coin and a Rs. 5 coin |
| D. | A Rs. 5 coin and a Rs. 10 coin |
| Answer» B. A Rs. 1 coin and a Rs. 2 coin | |
| 17. |
A By which congruency property are the two triangles PQS and PRS given in the following figure congruent? |
| A. | S.S.S. property |
| B. | S.A.S. property |
| C. | A.S.A. property |
| D. | R.H.S. property |
| Answer» C. A.S.A. property | |
| 18. |
\[\Delta \,ABC\cong \Delta FDE\] What is the measure of \[\angle F\]? |
| A. | \[50{}^\circ \] |
| B. | \[60{}^\circ \] |
| C. | \[80{}^\circ \] |
| D. | \[75{}^\circ \] |
| Answer» B. \[60{}^\circ \] | |
| 19. |
\[\Delta ABC\] is congruent to \[\Delta XYZ\]. Find the measures of \[\angle x\] and \[\angle y\] respectively. |
| A. | \[65{}^\circ ,\text{ }75{}^\circ \] |
| B. | \[75{}^\circ ,40{}^\circ \] |
| C. | \[75{}^\circ ,\text{ }65{}^\circ \] |
| D. | \[55{}^\circ ,\text{ }45{}^\circ \] |
| Answer» B. \[75{}^\circ ,40{}^\circ \] | |
| 20. |
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 |
| B. | The two triangles are necessarily congruent. |
| C. | The two triangle are congruent by A.A.A. congruency criterion. |
| D. | All of the above. |
| Answer» B. The two triangles are necessarily congruent. | |
| 21. |
Which of the following statements is CORRECT? Statement-1: 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. Statement-2: Two triangles are congruent if two sides and the included angle of the one must be equal to the corresponding two sides and included angle of the other. |
| A. | Only Statement-1 |
| B. | Only Statement-2 |
| C. | Both Statement-1 and Statement-2 |
| D. | Neither Statement-1 nor Statement-2 |
| Answer» C. Both Statement-1 and Statement-2 | |
| 22. |
\[\Delta ABC\] and \[\Delta DEF\] are as shown. By which condition of congruence is\[\Delta ABC\cong \Delta DEF\]? |
| A. | S.S.S. condition |
| B. | S.A.S. condition |
| C. | R.H.S. condition |
| D. | A.S.A. condition. |
| Answer» D. A.S.A. condition. | |
| 23. |
In the given figure, line PRT is parallel to SQN. If \[RS=8\text{ }cm\] what is the length of RO? |
| A. | 7 cm |
| B. | 3 cm |
| C. | 4 cm |
| D. | 6 cm |
| Answer» D. 6 cm | |
| 24. |
Which type of triangle is formed by \[BC=7.2\text{ }cm,\] \[AC=6\text{ }cm\] and \[\angle C=120{}^\circ \]? |
| A. | An acute angled triangle. |
| B. | An obtuse angled triangle. |
| C. | A right angled triangle. |
| D. | An isosceles triangle. |
| Answer» D. An isosceles triangle. | |
| 25. |
In \[\Delta PQR,\text{ }PS\bot QR,\text{ }\angle Q=\angle R\]. State by which property \[\Delta PSQ=\cong \Delta PSR\]? |
| A. | SAS property |
| B. | ASA property |
| C. | RHS property |
| D. | All i.e. (a), (b) and (c) |
| Answer» E. | |
| 26. |
In two triangles PQR and LMN, PQ = QR\[\angle P=\angle M\]and QR = LN,, then which of the following statements is CORRECT? |
| A. | Triangles are congruent only |
| B. | Triangles are isosceles only |
| C. | Triangles are both congruent and isosceles |
| D. | None of these |
| Answer» E. | |
| 27. |
If the given two Ales arc congruent, then what is true? |
| A. | \[AB=DE\] |
| B. | AC=DF |
| C. | \[BC=DF\] |
| D. | \[AB=DF\] |
| Answer» E. | |
| 28. |
In \[\Delta ABC,\] \[AB=AC\] and AD is perpendicular to BC. The property by which \[\Delta ADB\] is congruent to \[\Delta ADC\] is. |
| A. | SAS property |
| B. | SSS property |
| C. | RHS property |
| D. | AAA property |
| Answer» D. AAA property | |
| 29. |
The given figure shows \[\Delta ABC\] and \[\Delta PQR\] with \[AB=QR\]. What is the value of \[(AB+5BC+3AC+2RP-3PQ-QR)\]? |
| A. | 60 |
| B. | 55 |
| C. | 70 |
| D. | 25 |
| Answer» D. 25 | |
| 30. |
DIRECTION: Study the figure and information given below carefully and answer the following questions. CF and AE are equal perpendiculars on BD, BF = FE = ED. \[\Delta \,ABE\] is congruent to |
| A. | \[\Delta \,AED\] |
| B. | \[\Delta \,BFC\] |
| C. | \[\Delta \,CDF\] |
| D. | \[\Delta \,BCD\] |
| Answer» D. \[\Delta \,BCD\] | |
| 31. |
In the given figure, if \[\Delta OAP=\Delta OBQ,\]then which of the following is NOT true? |
| A. | AO = BO |
| B. | AP = SO |
| C. | PO = BO |
| D. | \[\angle APO=\angle BQO\] |
| Answer» D. \[\angle APO=\angle BQO\] | |
| 32. |
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. |
| B. | BD bisects \[\angle ADC\] |
| C. | BD bisects \[\angle BAD\] |
| D. | \[\Delta ABC\] and \[\Delta CBD\] are equilateral triangles. |
| Answer» C. BD bisects \[\angle BAD\] | |
| 33. |
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 |
| B. | S.S.S. property |
| C. | R.H.S. property |
| D. | A.S.A, property |
| Answer» D. A.S.A, property | |