B ench mark Test 3. Special Segments in Triangles. Answers. Geometry B enchmark T ests. 1. What is AC if } DE is a midsegment of the triangle?

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Howard Conley
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1 a te enc LSSON h m a rk T es ts More opy if needed ench mark Test Special Segments in Triangles 1. What is if } is a midsegment of the triangle? 11 1 nswers S ee grap h. a. b lac e an isosc eles right triangle w ith leg length a in a c oordinate p lane in a c onv enient w ay. ssign c oordinates to eac h v ertex. lot the midp oints of eac h side and lab el their c oordinates. c. 4.. triangle has c oordinates (0, 0 ), Q(0, 4s) and R(2s, 2s). a. What are the c oordinates of the midp oint of eac h side? b. triangle is formed b y joining the midp oints of the sides of triangle QR ly ing in the c oordinate p lane. S tate the lengths of all the sides of the inner triangle in simp lest radic al form. c. Is the inner triangle a right triangle? x p lain. RS is the p erp endic u lar b isec tor of } Q. ind R. R 4x 2x 1. } S Q opyright by Mcougal Littell, a division of Houghton Mifflin ompany. 1 enchmark T ests

2 a te ench mark Test c o n tin u e is the p erp endic u lar b isec tor of }. a. What segment lengths are eq u al? b. If is fi nd and.. ind m if there is enou gh information. x 2 2 2x 1 1 nswers a. b enc h m a rk T es ts 42 opyright by Mcougal Littell, a division of Houghton Mifflin ompany N ot enou gh information 7. T he p erp endic u lar b isec tors of n meet at. ind if there is enou gh information. O therw ise, state that there is not enou gh information.. is the inc enter of n. ind if there is enou gh information. O therw ise, state that there is not enou gh information. 4 enchmark T ests 17

3 a te enc LSSON h m a rk T es ts More opy if needed ench mark Test continued. In n, is the c entroid and 1. ind and. nswers S ee grap h. 10. T he v ertic es of nklm are K(0, 0 ), L(, ) and M(4, 2). ind the c oordinates of the c entroid. 11. T he v ertic es of a triangle are (1, 2), (, 2), and (4, 4). raw the triangle on the grid. Is the orthoc enter of the triangle inside, ou tside, or on the triangle? Ineq u alities and Triangles 12. Whic h side of this triangle is longest?. }. } y x. } 20. N ot enou gh information 1. n has 4,, and. L ist the angles in order from largest to smallest. 14. triangle has one side length of and another of length. Whic h is no t a p ossib le length for the third side? opyright by Mcougal Littell, a division of Houghton Mifflin ompany. 1 enchmark T ests

4 a te ench mark Test continued 1. Is it p ossib le to c onstru c t a triangle w ith the side lengths,, and? U se th e fo llo w ing fo r x ercises 1 and 17. x 2 1 2x S u p p ose x. Whic h of the follow ing mu st b e tru e?. m m. m m. m m. m m 17. S u p p ose m m. Whic h of the follow ing is no t a p ossib le v alu e for x? or the follow ing statement, w rite a temp orary assu mp tion y ou c ou ld mak e to p rov e the c onc lu sion indirec tly. If x is ev en and y is div isib le b y fi v e, then xy is div isib le b y 10. nswers enc h m a rk T es ts opyright by Mcougal Littell, a division of Houghton Mifflin ompany. ro po rtio ns in G eo metry 1 in. 1. S imp lify the ratio }. 4 ft } } 2 0. Y ou are b u ilding a rec tangu lar tab le top w ith an area of 24 sq u are feet, and the ratio of its length to its w idth is : 2. ind the w idth of the tab le.. feet. 4 feet. feet. feet 2 1. T he angles of a triangle hav e measu res in an ex tended ratio of 4 : :. ind the measu res of the three angles S olv e the p rop ortion. 7x } 20 2 } 0 2. S olv e the p rop ortion. 1 x } 2 1 x }. x }. x }. x }. x } 2 4. ind the geometric mean of 24 and.. 0. Ï }. 12 Ï }. 12 Ï } enchmark T ests 1

5 a te enc LSSON h m a rk T es ts More opy if needed ench mark Test c o ntinu e d 2. In the diagram, } }. Whic h of the follow ing is no t a tru e p rop ortion?. } 11 } x.. 11 } 11 } x } 11 1 x }. } 11 x 1 11 } 11 1 x x 2. map show s the distanc e b etw een a hou se and a c orner store as c m. a. If the sc ale of the map is 1 : 10 0, how far is the ac tu al distanc e? b. If eac h hou se has a y ard that is 20 m w ide, how many hou ses are b etw een the fi rst hou se and the groc ery store? 2 7. In the diagram, } N i } MQ, N O 4, O, and Q. ind MO. O x nswers 2. 2 a. 2 b N Q M 2. In the diagram,, i m i n, 40, 0, and 0. ind., 40 0 m 0 n opyright by Mcougal Littell, a division of Houghton Mifflin ompany. 2 0 enchmark T ests

6 a te ench mark Test c o ntinu e d 2. In the diagram, H ù G H. ind G. G H nswers enc h m a rk T es ts 2. Similarity 0. What is the sc ale fac tor b etw een the tw o regu lar hex agons? cm 7cm. 7 }. 1 }. 1 } 7. } 1 1. In the diagram, n, nlmn. ind x. opyright by Mcougal Littell, a division of Houghton Mifflin ompany. M 1 2x x L 12 N 2. In the diagram, w hic h of the follow ing mu st b e tru e?. n, n. n, n. n, n. n, n enchmark T ests 2 1

7 a te enc LSSON h m a rk T es ts More opy if needed ench mark Test c o n tin u e d. etermine w hether the triangles are similar. If they are, w rite a similarity statement. 4. In the diagram, w hic h of the follow ing does no t gu arantee nqr, ns T R? nswers R 2 Q S. QR ù S T R. Q i S T. Whic h of the follow ing is tru e? T. } R RT } 1. RQ ù RS T N 1. n, n. n, nlmn. n, nlmn. N o p air of similar triangles. x p lain how y ou w ou ld show nrs, nqs. Q R 4 4 L M 12 opyright by Mcougal Littell, a division of Houghton Mifflin ompany. S 2 2 enchmark T ests

8 a te ench mark Test c o n tin u e d 7. etermine w hether the tw o triangles are similar. If they are similar, w rite a similarity statement and fi nd the sc ale fac tor of T riangle to T riangle S nswers 7.. S ee grap h. enc h m a rk T es ts 120 R T Tria n g le Tria n g le. Q u adrilateral has the v ertic es (0, 2), (4, 0 ), (, ), and (1, 4). T he image of q u adrilateral after a dilation w ith sc ale fac tor of } 2 is q u adrilateral LMN. S k etc h b oth and LMN. opyright by Mcougal Littell, a division of Houghton Mifflin ompany. y x enchmark T ests 2

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N