3. A plot of land is about 13,000 ft by. A 1040 mi 2 B 4 mi 2 C 3939 mi 2 D 19,697 mi The proof that vertical angles 1 and 3 are
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1 Benchmark Test 1 1. A frame is 45 in. by 32 in. How many square feet are in the area of this frame? A 120 ft 2 B 100 ft 2 C 10 ft 2 D 12 ft 2 2. The circumference of circle P is 800 mm, the circumference of circle Q is 200 cm, and the circumference of circle R is 4 m. What is the sum of the distances around each circle? 3. A plot of land is about 13,000 ft by 8000 ft. Approximately how many square miles is this? Round to the nearest whole number. A 1040 mi 2 B 4 mi 2 C 3939 mi 2 D 19,697 mi 2 4. The proof that vertical angles 1 and 3 are congruent is started below. F 24.2 m G 7.5 m H 6.8 m J 31.4 m /1 1 / Angles 1 and 2 are supplementary angles. /2 1 / Angles 2 and 3 are supplementary angles. Which statement might be next? F /1 1 /2 5 /2 1 /3 G /3 1 / H /1 1 /2 5 /2 1 /1 J /2 1 /
2 5. What could also be proved true from the diagram in Exercise 4? A /1 5 /2 B /3 5 /4 C /2 5 /3 D /2 5 /4 8. Which figure below shows a pair of supplementary angles that are not adjacent? F Given the diagram below, which of the following statements is NOT true? P Q G S T R * F PR ) ) and * SQ ) ) intersect in point T. G PT and TQ are both rays. H ST ) and PR ) are both segments. J PT and QT are opposite rays. H In the figure below, you cannot assume that 9. Y J 110 X Z P T W A /XPT and /ZPW are vertical angles B m/ypw C Points T, P, and Z are collinear D * XW ) and * TZ ) intersect at point P 10
3 9. /TUV and /VUW are adjacent complementary angles. If m/tuv 5 80, what is m/vuw? A 10 B 90 C 70 D What is being constructed? 10. Which item is never used to make constructions? F straightedge G measurement markings on a ruler H compass J pencil 11. Which diagram shows the construction of an angle bisector? A B C F perpendicular bisector G parallel lines H circle J copy of an angle 13. What is the distance beteen points A(1, 9) and B(4, 22)? A!58 C!130 B 58 D AB has endpoints A(2, 4) and B(8, y). If AB is 10, what is the value of y? F 8 H 64 G 12 J Q is the midpoint of PR. What are the coordinates of point R? y 4 Q D 4 4 x P 4 A (6, 5) B (5, 6) C (4, 5) D (2, 5) 11
4 16. A rectangular picture has an area of 30 square inches. The length of the picture is 1 inch more than the width. What is the perimeter of the picture? F 5 in H 11 in G 6 in J 22 in 17. Given that the figure below is a quarter of a circle, which of the formulas could be used to find the length of the curved part? A pr 4 pr B 2 C pr D pr The perimeter of a rectangle is 100 yd. If its width is four times its length, what is the area? F 625 yd 2 H 400 yd 2 G 525 yd 2 J 225 yd A regular postage stamp is approximately 2 centimeters wide and 3 centimeters tall. If there are 5 rows of 6 stamps on a sheet, what is the approximate area of the sheet? A 54 cm C 180 cm B 54 cm 2 D 180 cm What is the difference between the areas of a square with a side length of 4 units and a circle with a diameter of 4 units? Round your answer to the nearest tenth. F p units H 3.4 units G 3.4 units 2 J 0 units What is being proven in the proof below? 1. m/1 1 m/ Given 2. m/2 1 m/ Given 3. m/1 1 m/ Transitive m/2 1 m/3 Property of Equality 4. m/1 5 m/3 4. Subtraction Property of Equality 5. /1 > /3 5. Angles with the same measure are congruent. A Angles 1 and 3 are equal when angle 2 is a complement of both angles 1 and 3. B Angles 1 and 3 are equal when angle 2 is a complement of angle 1. C Angles 1 and 3 are equal when angle 2 is a complement of angle 3. D Angles 1, 2, and 3 are right angles. 22. In the proof below, what reason is missing? Given: /1and /2 are right angles. Prove: /1 > /2. 1. /1 and /2 are 1. Given right angles 2. m/ and 2. Definition of m/ a right angle. 3. m/1 5 m/ /1 5 /2 4. Angles with the same measure are congruent. F Subtraction Property of Equality G Addition Property of Equality H Transitive Property of Equality J Angles with the same measure are congruent. 12
5 23. If AQ is a perpendicular bisector of CB, the distance from A to C is the same as the distance from A to B. The proof is started below. 25. In which situation is it necessary to measure from J to K? 1. AQ is 1. Given perpendicular bisector of CB 2. AQ is ' CB 2. Definition of perpendicular bisector. 3. CQ > QB 3. Definition of perpendicular bisector. 4. AQ > AQ 4. 9 What property is shown in the last statement? A Symmetric B Transitive C Reflexive D Substitution 24. What construction is being performed based on what is shown? A When bisecting /BAC B When copying angle /BAC C When drawing a segment JK D When creating a triangle with segment JK 26. When constructing the perpendicular bisector of PQ, what would be the correct first step? F Put the compass point on point P and draw a long arc. Be sure the opening is equal to 1 2 AB. G Put the compass point on point P and draw a short arc. Be sure the opening is equal to 1 2 AB. H Put the compass point on point P and draw a long arc. Be sure the opening is greater than 1 2 AB. J Put the compass point on point P and draw a short arc. Be sure the opening is greater than 1 2 AB F Bisecting a segment G Drawing a parallel line H Copying a segment J Drawing a perpendicular bisector 13
6 27. Which statement and reason should go next in the following paragraph proof? 29. Find the value of x. 3x (x 28) Given: /1 and /2 are supplementary m/2 5 m/3 Prove: /1 and /3 are supplementary We are given that /1 and /2 are supplementary. By the definition of supplementary, m/1 1 m/ m/2 5 m/3 is given. A /1 and /3 are supplementary by the definition of supplementary. B m/1 1 m/ by the Substitution Property of Equality. C /2 and /3 are not supplementary by the definition of supplementary. D m/3 5 m/2 by the Symmetic Property. 28. In the figure below, if m/axc 5 10x, then m/bxd 5 9. A X B A x 5 7 B x 5 14 C x D x Name pairs of congruent angles in the figure. I. /EIF and /GIH II. /GIF and /GIH III. /EIF and /GIF IV. /EIG and /FIH E I H F G F I and IV G II and III H I and II J I only C D F 10x H x G x J x STOP 14
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