2. The vertices of Δ ABC are A( 1, 2), B( 1,2), and C(6,0). Which conclusion can be made about the angles of Δ ABC?

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1 1 Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P and R? A. Planes P and R are skew B. Planes P and R are perpendicular. C. Planes P and R are parallel. D. Plane P intersects plane R but is not perpendicular to plane R. 2. The vertices of Δ ABC are A( 1, 2), B( 1,2), and C(6,0). Which conclusion can be made about the angles of Δ ABC? A. m<a = m<b B. m<a = m<c C. m<acb = 90 D. m<abc = 60 3 A triangle whose three sides are equal is called?to report click on question a b c d Right angle triangle Equilateral Triangle Isosceles Triangle None of the above 4 A triangle which has one angle of 90 degree is known as?to report click on question a b c d Right angle triangle Equilateral Triangle Isosceles Triangle None of the above 5 A quadrilateral whose only two sides are parallel is known as?to report click on question a Square

2 b c d Rectangle Trapezoid Polygon Answer of MCQ 1-c 2-a 3-b 4-a 5-c _ 1. If BCDE is congruent to OPQR, then is congruent to a. b. c. d. 2. Use the information given in the diagram. Tell why and A B D C a. Reflexive Property, Given b. Transitive Property, Reflexive Property c. Given, Reflexive Property d. Reflexive Property, Transitive Property 3.

3 a. b. c. d. 4. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale. g 38 b 5 d 4 f 3 e 52 c a. 4 b. 5 c. 3 d Given and, find and a. 22 b. 11 c. 10 d Justify the last two steps of the proof. Given: and

4 Prove: R S T U Proof: Given Given a. Symmetric Property of ; SSS c. Reflexive Property of ; SSS b. Reflexive Property of ; SAS d. Symmetric Property of ; SAS 7. State whether and are congruent. Justify your answer. 7 7 a. yes, by either SSS or SAS b. yes, by SSS only

5 c. yes, by SAS only d. No; there is not enough information to conclude that the triangles are congruent. 8. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. 9. From the information in the diagram, can you prove? Explain.

6 ( a. yes, by ASA c. yes, by SAS b. yes, by AAA d. no 10. What else must you know to prove the triangles congruent by ASA? By SAS? A B ( D C a. ; c. ; b. ; d. ; 11. Name the theorem or postulate that lets you immediately conclude A B D C a. SAS b. ASA c. AAS d. none of these 12. Supply the missing reasons to complete the proof. Given: and

7 ( ( Prove: Q S R P T a. ASA; Substitution c. AAS; CPCTC b. SAS; CPCTC d. ASA; CPCTC 13. Supply the reasons missing from the proof shown below. Given:, Prove: A B D C

8 a. ASA; CPCTC c. SSS; Reflexive Property b. SAS; Reflexive Property d. SAS; CPCTC 14. The octagon in the figure is equiangular and. Find. A B C a. 135 b. 45 c. 30 d In an A-frame house, the two congruent sides extend from the ground to form a 34 angle at the peak. What angle does each side form with the ground? a. 156 b. 146 c. 73 d What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42?

9 a. 69 b. 84 c. 138 d Find the value of x. The diagram is not to scale. S R (3x 50) (7x) T U a. b. c. d. none of these 18. Two sides of an equilateral triangle have lengths and. Which of or could be the length of the third side? a. neither 10 x nor 6x + 5 c. both 10 x and 6x + 5 b. 10 x only d. 6x + 5 only 19. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement? A B C D

10 a. Yes;. b. Yes;. c. Yes;. d. No, the triangles cannot be proven congruent. 20. is perpendicular to at between A and D. By which of the five congruence statements, HL, AAS, ASA, SAS, and SSS, can you conclude that a. HL, AAS, ASA, and SAS c. HL and ASA b. HL, AAS, and ASA d. HL, AAS, ASA, SAS, and SSS Answer of MCQ 1. ANS: D 2. ANS: A 3. ANS: D 4. ANS: C 5. ANS: C 6. ANS: C 7. ANS: A 8. ANS: B 9. ANS: A 10. ANS: B 11. ANS: A 12. ANS: D 13. ANS: D

11 14. ANS: B 15. ANS: C 16. ANS: D 18. ANS: B 19. ANS: B 20. ANS: A 1 POLYGON WITH 4 SIDES A. Parallelogram B. Quadrilateral C. Base angles D. Midsegment 2 A(n) is a quadirlateral with exactly one pair of parallel sides. A. Rectangle B. Trapezoid C. Parallelogram D. Midsegment 3 A(n) is a parallelogram with four congruent sides and four right angles. A. Rectangle B. Square C. Parallelogram D. Square 4 Name the quadrilateral one pair of parallel sides. Consecutive angles that share a leg are supplementary.

12 A. Square B. Trapezoid C. Rectangle D. Parallelogram 5 A(n) is a trapezoid whose nonparallel opposite sides are congruent. A. Trapezoid B. Rectangle C. Midsegment of a trapezoid D. Isosceles trapezoid. 6 Name the quadrilateral (legs are congruent) Base angles are congruent Diagonals are congruent. A. Parallelogram B. Isosceles trapezoid C. Rectangle D. Quadrilateral 7 Name the quadrilateral No sides parallel. 2 pair of consecutive sides congruent. Diagonals of a are perpendicular (One bisects the other). A. Kite B. Quadrilateral C. Trapezoid D. Kite 8 1. Parallelogram 2. Right angles in corners. Diagonals bisect each other. Diagonals are congruent. Two pairs of sides are congruent. A. Square B. Rectangle C. Midsegment D. Trapezoid

13 9. So how many points does a tanget line in to the circle touch on the circle. A. 2 B. 1 C. 0 D. Depending on the circle size 10. Will there be congruous arcs on the circle. A. Depending on arc size B. It depends on size of the circle C. Yes D. No Answer of MCQ 1-b 2-b 3-d 4-b 5-d 6-b 7-a 8-b 9-b 10-c 1 A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is: A. 12 cm 3 B. 15 cm 3 C. 16 cm 3 D. 20 cm 3 2. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is: A. 75 cu. M B. 750 cu. m C cu. M D cu. m

14 3. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is: A. 720 B. 900 C D cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be: A. 84 B. 90 C. 168 D A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is: A. 3.6 kg B kg C. 36 kg D kg 6 A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: A. 12 kg B. 60 kg C. 72 kg D. 96 kg

15 7. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m 3, then the rise in the water level in the tank will be: A. 20 cm B. 25 cm C. 35 cm D. 50 cm 8. The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface. A. 30П m 2 B. 40П m 2 C. 60П m 2 D. 80П m 2 9. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: A. 49 m 2 B. 50 m 2 C m 2 D. 55 m A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m 3 ) is: A B C. 6420

16 D The curved surface area of a cylindrical pillar is 264 m 2 and its volume is 924 m 3. Find the ratio of its diameter to its height. A. 3:7 B. 7:3 C. 6:7 D. 7:6 12. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is: A. 90 cm B. 1 dm C. 1 m D. 1.1 cm 13. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm? A cm 2 B. 462 cm 2 C cm 2 D. None of these 14. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube? A. 2:1 B. 3:2

17 C. 25:18 D. 27: How many bricks, each measuring 25 cm x cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? A B C D Answer of MCQ 1-a 2-b 3-c 4-a 5-b 6-b 7-b 8-c 9-a 10-b 11-b 12-b 13-c 14-c 15-c 1. The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is: A B C D An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: A. 2% B. 2.02%

18 C. 4% D. 4.04% 3. The ratio between the perimeter and the breadth of a rectangle is 5:1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? A. 16 cm B. 18 cm C. 24 cm D. Data inadequate E. None of these 4. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is: A. 40% B. 42% C. 44% D. 46% 5. A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road? A m B. 3 m C m D. None of these

19 6. The diagonal of the floor of a rectangular closet is feet. The shorter side of the closet is feet. What is the area of the closet in square feet? A B C. 27 D A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is: A. 10% B % C. 20% D. 28% 8. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? A. 20 B. 24 C. 30 D The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be: A. 9 cm

20 B. 18 cm C. 20 cm D. 41 cm 10. What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad? A. 814 B. 820 C. 840 D The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is: A m 2 B m 2 C m 2 D m The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area? A. 25% increase B. 50% increase C. 50% decrease D. 75% decrease

21 13. The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the per metre is Rs. 5300, what is the length of the plot in metres? A. 40 B. 50 C. 120 D. Data inadequate E. None of these 14. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required? A. 34 B. 40 C. 68 D A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is: A. Rs. 456 B. Rs. 458 C. Rs. 558 D. Rs. 568 Answer of MCQ 1-b 2-d 3-b 4-c 5-b 6-c 7-d 8-c 9-b 10-a 11-d 12-b 13-e 14-d 15-c

22 1. A and B together have Rs If 4 15 of A's amount is equal to 2 5 amount does B have? of B's amount, how much A. Rs. 460 B. Rs. 484 C. Rs. 550 D. Rs Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: A. 2:5 B. 3:5 C. 4:5 D. 6:7 3. A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs more than D, what is B's share? A. Rs. 500 B. Rs C. Rs D. None of these 4. Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? A. 2:3:4

23 B. 6:7:8 C. 6:8:9 D. None of these 5. In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is: A. 20 litres B. 30 litres C. 40 litres D. 60 litres 6 The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? A. 8:9 B. 17:18 C. 21:22 D. Cannot be determined 7. Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary? A. Rs. 17,000 B. Rs. 20,000 C. Rs. 25,500 D. Rs. 38, If 0.75:x::5:8, then x is equal to:

24 A B. 1.2 C D The sum of three numbers is 98. If the ratio of the first to second is 2:3 and that of the second to the third is 5:8, then the second number is: A. 20 B. 30 C. 48 D If Rs. 782 be divided into three parts, proportional to 1 2 : 2 3 : 3 4, then the first part is: A. Rs. 182 B. Rs. 190 C. Rs. 196 D. Rs. 204 Answer of MCQ 1-b 2-c 3-c 4-a 5-d 6-c 7-d 8-b 9-b 10-d