UV =. If the area of GEOMETRY INDIVIDUAL TEST. 4. Δ RST is 100, then what is the area of A. 25 B. 200 C. 400 D E. NOTA

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1 1. Δ T has three angles with degree measures 3x 12, 36 + x and 2x Which set f adjectives describes the triangle? A. right, issceles B. btuse, issceles C. right, scalene D. acute, equilateral 2. Tw chrds in a circle f radius 5 inches are inches and 3 inches frm the circle s center, respectively. What is the sum f the lengths f the tw chrds, in inches? A. 5 B. 7 C. 12 D NOTA means Nne f These Answers and shuld be chsen if chices A, B, C and D are nt crrect. Diagrams may nt be drawn t scale. ( x 10) ( x+ 2 y) 1. ΔT ~ Δ UVW. UV =. If the area f Δ T is 100, then what is the area f Δ UVW? A. 25 B. 200 C. 00 D Which f the fllwing side lengths f triangles can be the side lengths f a right triangle? A. 12 cm, 15 cm, 20 cm B. 2 in., 3 in., 6 in. C. 6 m, 6 2 m, 6 3 m D. 6 dm, 6 dm, 6 3 dm 6. The value f n (a natural number) is evenly divisible by 2, 3,, 5, 6, 8, 10, 12 and 15. Find the least pssible value f n and then give the measure f ne interir angle f the regular plygn which has n sides. A. 178 B. 177 C. 176 D A triangle has sides f lengths 3, and x. Which f the fllwing must be true f the length x? Tw adjacent cplanar angles which share a nn-cmmn side have degree measures ( x 10) and ( x+ 2 y). Their nn-cmmn sides frm ppsite rays. Give the value f x+ y. A. 1< x < 7 B. 3< x < C. 3 x D. x = 5 A. 95 B. 90 C. 80 D. 70

2 8. 9 gap dg 20 A dg is leashed t ne crner f a fenced 9 x 20 rectangular back-yard. There is shade ver the entire area, and cpius fd and water (safe and happy dg). His leash is 10 feet lng. The 20 side runs east and west. At the nrth-west crner f the enclsure there is a 1-ft gap in the fence s the nrth side is nly 19 in length, and the dg can fit thrugh this gap. What is the farthest east that the dg can ram frm the 9 ft wall (west) when he is utside f the fence? Disregard dg dimensins. A. ( ) ft B. (10 82 ) ft C. (11 82 ) ft D. 1 ft 9. The wners f the dg frm #8 later fixed the gap in the fence by mving the nrth side in by abut 0.3 ft and making the east-west sides each a full 20 ft. Nw the dimensins f the rectangular fence are 20 by 5 3. Use the new dimensins f the fenced area, and disregard the dg dimensins. The area f the fenced-in enclsure that the dg can ram, still n the same length leash, is ( Pπ + Q ) square feet, fr a prime number and P and Q reduced fractins. Give 2PQ. 10. Will the area that the dg can ram change if the 10 leash is fixed at a pint n the lng side f the fence, 5 feet t the east f its previus fixed 5 3 anchr? 5 15 A. N. The area he can ram will nt change. B. Yes. The area will increase by 25 3 sq ft. C. Yes. The area will increase by sq. ft D. Yes. The area will increase by 6 3 sq. ft. 11. Parallelgram TU has tw f its angles with measures (3x + 12) and ( x + 6). Which must be true? A. TU may be a rectangle but des nt have t be. B. TU is a rectangle nly if the tw given measures are f ppsite angles. C. TU is a rectangle nly if the tw given measures are f cnsecutive angles. D. TU is a rectangle. A B C D. 1650

3 12. A standard three-legged stl had ne leg chewed by the classrm hamster. One leg is nw 1 inch shrter than the ther tw legs, which are still cngruent t each ther. The pints at the end f each f the legs are, and T (after the chewing incident)., and T are... A. cllinear but nt cplanar B. cplanar but nt cllinear C. neither cplanar nr cllinear D. bth cplanar and cllinear 13. Δ T has area 20 and =6. T=8. Give the distance frm pint t side T? A. 5 B. 6 C. 8 D. 10 T chewed 15. ( y + 0) Q 60 P (2 x ) Δ PQ is inscribed in the circle shwn abve, with ( y + 0) the measure f QP ª (arc), and m P= 2x and m Q= 60. Which gives the relatinship between the values f x and y? A. y = 200 x B. y = x C. y = 200 2x D. y= x 1. A linear pair is drawn n a plane. It cnsists f angles T and TU. T is supplementary t EFG. Which statement(s) must be true? I. TU is supplementary t EFG. II. TU and EFG frm a linear pair. III. T and EFG frm a linear pair. IV. EFG TU. V. T and EFG are cplanar. A. II, III, V nly B. I, II, V nly C. III, V nly D. IV nly 16. In trapezid UT shwn P TU and interir angle measures are given in the diagram. Give the value f x. 60 ( y ) x T U A. 30 B. 120 C. 130 D. 10 ( y + 10)

4 17. A C 20. U T BC is a diameter f the circle shwn, and mab ª = mcd ª = 90. If BC=0 then give the area f the shaded segment bunded by BD and ª BD. B A. 00π 200 B. 100π 200 C. 100π D. 100π 100 D Transversal W suur suur suur intersects T and suur VX suur at pints and W respectively. T P VX. U, and W are cllinear. 2 m UT = ( y 10y+ 18), m WT x x 2 = ( 1 + 3), and m WX V W X = (2x+ 17). Give the value f x y A. 9 B. 8 C. 7 D A regular hexagn has the same perimeter as the circumference f a circle P. If the circle P has area 9, then find the area f the hexagn. A. 3 π D. 2 π B. 9 π 3 C. 5 3 π 21. Δ TY has side lengths 6, 8 and Which describes the triangle? A. acute B. btuse C. right D. nt a triangle 19. hmbus TU has perimeter 52 and the length f ne f its diagnals is 2. What is the length f the ther diagnal f TU? P 22. In Δ P, Q is the altitude t hyptenuse P. If Q=15 and P=10 then find Q. Q A. 10 B. 12 C. 1 D. 26 A. 20 B. 8 C. 5 3 D. 6 2

5 23. V egular hexagn WLZV has sides with lengths 10 each. ectangle TYXU has. vertices n the midpints f sides W, WL, VZ and V as shwn. What is the area in the shaded trapezid TU? A D U X Z B C L T Y W 25. Tangent ray uuur U intersects secant segment T at, and is T the pint f tangency f the ray. T intersects the circle at pint U. If =10 and U=2, then find UT. A. 50 B. 8 C. 6 D In right Δ T, A is the height t hyptenuse T. A = 6, A = ( a + ) and AT = a, then give the length f side T. A. 12 B. 1 C. 16 D ΔT ~ Δ MNP : = 2 5, T = 2 15, T = 5 and MN = What is m M in degrees? 2. A regular plygn has ne exterir angle with measure m and ne interir angle with measure ( 2m + 5), bth in degrees. Hw many sides des the plygn have? A. 12 B. 11 C. 10 D. 8 A. 5 B. 60 C. 90 D Issceles triangle T has =T. m = 50 and m = (2x+ 10). Give the value f x. A. 20 B. 25 C D. 30

6 29. A circle inscribed in a regular pentagn has area 36π. The area f the pentagn is P(tan( Q ). Give the value f P+ Q. A. 232 B. 216 C. 96 D Δ T and Δ ABC are drawn with m = m B, T AC and T BC. Which f the fllwing statements must be true? A. ΔT Δ ABC by A Therem B. ΔT and ΔABC are nt cngruent C. ΔT Δ ABC by if AB D. ΔT Δ ABC by AA Therem if T C.