Grade 9

Department of Education DIVISION

Region III

OF

PA M PA N G A

City of San Fernando

THIRD PERIODIC TEST IN MATHEMATICS GRADE 9 DIRECTION: ON YOUR ANSWER SHEET, WRITE THE LETTER OF CORRECT ANSWER.

1. It is a quadrilateral with exactly one pair of parallel sides. A. parallelogram B. rectangle C. square D. trapezoid 2. Which statement is true? A. All rectangles are squares. B. All quadrilaterals are squares. C. All parallelograms are quadrilaterals. D. All quadrilaterals are parallelograms. 3. Which of the following quadrilaterals does not belong to the group? A. Kite B. Rectangle C. Rhombus D. Square 4. Which of the following quadrilaterals is NOT a parallelogram? A. C.

B.

D.

5. Which of the following conditions is NOT enough to conclude that a quadrilateral is a parallelogram? A. The diagonals are perpendicular bisector of each other. B. Both pairs of opposite angles are congruent and supplementary. C. One pair of opposite sides is both congruent and parallel to each other. D. The diagonals are congruent, and the opposite sides that make up a pair are parallel to each other. 6. Which of the following is a sufficient condition for quadrilateral CALM to be a parallelogram? A. CM // LA and ML  CA

M

C

B. CM // LA and MA  LC C. ML // CA and ML  CA D. LMC  CAL and ML  CA

L

A

For numbers 7-9, quadrilateral LIKE is a parallelogram. L

I S

K

E

7. If LS = 18, find KI. A. 9 B. 18 C. 36 D. cannot be determined 8. If KE = 25 and KI = 24, find SI. A. 12 B. 24 C. 25 D. cannot be determined 9. If mLKE = 70, find mLIE. A. 35 B. 70 C. 110 D. cannot be determined 10. Given parallelogram ABCD with mA = 4x + 15 and mC = 6x – 27. What is mB? A. 21 B. 22 C. 81 D. 99 11. Which of the following information serves as a sufficient condition for classifying quadrilateral MALE as a rectangle? A. LM & AE bisect each other B. LM & AE bisect each other and LM is perpendicular to AE C. LM & AE bisect each other and LM is congruent to AE D. LM & AE bisect each other, LM is perpendicular to AE, and LM is congruent to AE 12. Which two properties of the rhombus DO NOT hold true for other parallelogram? A. Diagonals are congruent and bisect each other. B. Diagonals are perpendicular and each bisects the angles of the parallelogram C. Diagonals are perpendicular and congruent D. Diagonals are perpendicular and bisect each other 13. Given OS is the mid segment of triangle HEU, OS = x + 8 and HE = 3x + 12. Find x. A. x = 2 B. x = 3 C. x = 4 D. x = 5 14. The sail of a small boat is an equilateral triangle. If the mid segment of the triangle is 5 meters. Find the perimeter of the triangle. A. x = 10m B. x = 20m C. x = 30m D. x = 40m 15. Given BE = 3x + 2 and BD = 2(4x – 5). Find BD. A. 35 B. 41 C. 46 D. 52 16. Find the value of x A. x = 15 B. x = 30

C. x = 45 D. x = 60 17. If the perimeter of an isosceles trapezoid is 194 cm and the bases are 63 cm and 49cm, how long is each leg? A. 112 cm B. 96 cm C. 82 cm D. 41 cm 18. A cross section of a water trough is in the shape of a trapezoid with bases measuring 2m and 6m. What is the length of the median of this trapezoid? A. 2 m B. 4 m C. 5m D. 8m 19. Given: isosceles trapezoid TRAP with median GO. T R G O P A If TR = x + 2, PA = x – 14 and GO = 36. How long is PA? A. 28 B. 36 C. 42 D. 72 20. Which proportion leads to the equation ta = yo? A. t/y = o/a B. t/a = y/o C. y/o = t/a D. a/o = t/y 21. If the first, second, and third term in a proportion are 5, 7, and 30, respectively, what is the fourth proportional? A. 40 B. 42 C. 44 D. 45

For numbers 22- 25, ST // UV W

S U 22. WS = 5, SU = 7, WT = 10, Find TV. A. 12 B. 13 C. 14 D. 15 23. WU = 15, SW = 12, UV = 10, find ST. A. 12 B. 10 C. 8 D. 6 24. VW = 28, SW = 6, WT = 10, find UW.

T V

A. 20 B. 56/5 C. 84/5 D. 25 25. WT = 22, WV = 36, WS = 11, find SU. A. 15/7 B. 7 C. 24/5 D. 25 26. Given the figure, which ratio is equivalent to IH/ IJ? J

I

H F G A. FG/ GH B. IG/ IH C. JH/ FG D. HG/ FG 27. If  GHI  JKL, then GI/ GH is equal to A. JK/ KL B. JL/ JK C. JK/ JL D. KL/ JL 28. Which is NOT true about similar triangles? C. Similar triangles are congruent. B. The corresponding angles are congruent. A. The corresponding sides are proportional. D. Triangles similar to the same triangle are similar. 29. If two triangles are similar and the ratio of the corresponding sides is 5: 8, what is the ratio of the corresponding areas? A. 5 : 8 B. 2 : 3 C. 5/8 D. 25/64 30. If the ratio of the areas of two similar polygons is 8/16, what is the ratio of their areas? A. 8/16 B. ½ C. 64/256 D. ¼ 31. If the ratio of the corresponding sides of two similar triangles is 4/5 and the perimeter of the smaller triangle is 120m, what is the perimeter of the larger triangle? A. 60m B. 100m C. 120m D. 150m For numbers 32 – 40

32. If x = 5 and y = 10, find h. A. −5 √ 2 B.

√2

C.

5 √2

D.

15 √2

33. If y = 3 and c = 12, find b. A. 2 B. 4 C. 6 D. 8 34. If a = 20 and c = 25, find x. A. 10 √ 5 B.

15 √5

C.

10 √2

D.

15 √2

35. A vacant lot has the shape of 450 – 450 – 900 triangle. If the longest side of this lot measures 52 meters. Find the perimeter of the lot. A. (104 + 52 √ 2 )m

√ 2 )m (30 + 52 √ 2 )m (10 + 52 √ 2 )m

B. (52 + 52 C. D.

36. Find the value of x. A. −5 √ 2 B.

√2

C.

5 √2

D.

15 √2

37. Use the given triangle to find x. A. 2 √ 3 B.

5 √3

C.

8√3

D.

10 √3

38. Find the perimeter of a square whose diagonal is 9 √ 2 cm long. A. 15 cm B. 21 cm C. 26 cm D. 36 cm 39. Which of the following pairs of triangle are similar? A. B. C.

D.

40. In a 300 – 600 – 900 triangle, which side is the shortest? A. The side opposite the 600 angle B. The hypotenuse C. The included side of the acute angle D. The side opposite the 300 angle For 41 – 42. Identify the theorem that makes the following triangles similar. 41.

A. SSS Similarity Theorem B. SAA Similarity Theorem C. SAS Similarity Theorem D. None of the above

42.

A. SSS Similarity Theorem B. SAA Similarity Theorem C. SAS Similarity Theorem D. None of the above

43. Shane marched 3m eats and 6m north. How far is he from his starting point? A. 4.4 m B. 6.71m C. 9.8 m D. 12m 44. John leaves schools to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school? A. 10 blocks B. 8 blocks C. 6 blocks D. 4 blocks 45. A 12 ft ladder is placed four feet from the base of a wall. How far up the wall will the ladder reach? A. √ 2 B.

2 √2

C.

6√2

D.

8 √2

46. A 13 ft ladder is placed 5 ft away from the wall. The distance from the ground straight up to the top of the wall is 13 feet. Find the height of the wall. A. 10 ft B. 12 ft C. 14 ft D. 16 ft 47. If the square of the hypotenuse of an isosceles triangle is 128 cm2, find the length of each side. A. 6 ft B. 8 ft C. 10 ft

D. 12 ft 48. A person 1.6m tall casts a shadow of 4.0 m at the same time that a flagpole casts a shadow of 4.2m. What is the length (h) of the flagpole? A. 1.4 m B. 1.68m C. 1.8 m D. 2m 49. Mae is standing 28 inches from a street lamp. If her height is 6 feet and 2 inches and the street lamp is 18 feet high, find the length of her shadow. A. 14. 59 in B. 14.8 in C. 15.2 in D. 15. 8 in 50. A yardstick and a telephone pole stand perpendicular to the ground. If the shadow of the yardstick is 12 ft and is located 24 ft from the pole, how tall is the telephone pole? A. 6 ft B. 7 ft C. 8 ft D. 9 ft