ommon ore Readiness ssessment 4 1. Use the diagram and the information given to complete the missing element of the two-column proof. 2. Use the diagram and the information given to complete the missing element of the two-column proof. Given: is an exterior angle of. rove: m = m + m Statements Reasons 1. is an 1. Given exterior angle of. 2. and 2. ngles that are form a straight supplementary. angle are supplementary. 3. m + 3. Definition of m = 180 supplementary angles 4. m + 4. Triangle ngle m + Sum Theorem m = 180 5. 9 5. Transitive roperty of quality 6. m = 6. Subtraction m + roperty of m quality m Q = 180 - m m = 180 - m m = 180 - m Q D m + m = m + m + m Given: Triangle with _, bisects. rove: # Statements Reasons 1. _, 1. Given bisects. 2. _ 2. Definition of angle bisector 3. _ 3. Reflexive roperty of congruent 4. _ 4. SS 5. _ 5. orresponding arts of congruent Triangles are congruent 6. and 6. ngles that are form a straight supplementary. angle are supplementary. 7. and 7. 9 are right angles. 8. # 8. Definition of perpendicular lines F ngles opposite congruent sides of a triangle are congruent. G ongruent supplementary angles are right angles. H # J Triangle ngle Sum Theorem 167 HSIM14_N_R_M1_M4.indd age 167 27/06/13 8:55 M ehi-6 /129/00739_N/HSIM14_NILLRIS/NILLRY/HSIM14/Math_01//Layout/In...
3. uilders are replacing the congruent roofs on House and House. What is the measure of Z on House? 115 65 25 115 65 D 180 4. lassify the triangle produced by the following construction. Note that the final step is not shown. I. II. House 115 W Z House Y 6. What is the first step in constructing the perpendicular to line / at point N? N F Draw an arc above point N. G onstruct a 90 angle with vertex at point N. H Mark two points on line l that are equidistant from N. J With the compass at point N, draw a circle. 7. In the construction of a line parallel to line m though point, what must be true about the construction of 1 and Y? 1 III. Y m IV. F equilateral G right H right and isosceles J obtuse and isosceles 5. Find the value of x. 1 and Y must be acute. 1 and Y must be obtuse. 1 and Y must be congruent. D 1 and Y must be supplementary. 8. If these two triangular puzzle pieces are to be made congruent, what must be the value of z? (2x 5) (x 12) F 64 H 136 G 116 J 26 x = 3.5 x = 8.5 x = 7 D x = 17 168 HSIM14_N_R_M1_M4.indd age 168 27/06/13 8:55 M ehi-6 /129/00739_N/HSIM14_NILLRIS/NILLRY/HSIM14/Math_01//Layout/In...
9. Given and D bisect each other at point, which congruence theorem would you use to prove _ D? D 12. In the figure, QR _ RS by SS. What pair(s) of sides can you conclude are congruent by T? Q R HL S SS D SSS S 10. Under the conditions stated below, what postulate implies that GHJ and MHO are congruent? OH _ JH, O _ J O I. QR _ SR II. QR _ S III. QR _ R F I only G I and II H II only J II and III G H F S G SS H SSS J S M 11. Given that HF is the bisector of HG and H = HG, which congruence statement can be used to prove that FH _ GFH? J 13. If _ YZ and = 3, = 6 and = 4, what is the length of Z? 3 4 5 D 6 14. Given YZ below, what is m Y? Y H S SS HL D SSS G F Z F 30 G 60 H 90 J cannot be determined 169 HSIM14_N_R_M1_M4.indd age 169 27/06/13 8:55 M ehi-6 /129/00739_N/HSIM14_NILLRIS/NILLRY/HSIM14/Math_01//Layout/In...
15. Under the conditions JL _ NL and KL _ ML, what theorem or postulate implies MJL _ KNL? J SSS SS S D S K 16. Identify the congruence transformation that maps to DF. D L y M N 18. SU, RW, and VT are medians. Find the length of T. R V 16 F 9 H 16 G 14 J 18 19. What is the point of concurrency of the lines containing the altitudes of a triangle? circumcenter incenter orthocenter D centroid 9 7 U S W T F O x 20. Which of the following can be used to inscribe a circle in a triangle? F circumcenter G incenter H orthocenter J centroid F T (4, 0) r (270,) G R y@axis r (90,) R x@axis H r (90,) R x@axis J T (1, -1) r (90,) 17. Find the value of x. 21. What is the center of a circle circumscribed about a triangle with vertices ( -2, 2) (2, -2), and (6, 2)? (2, 2) (0, 2) (2, 0) D (0, 0) 2y 4 y 3 3 6 7 D 12 2x y 5 22. Suppose you are asked to complete the following indirect proof. Given: n is negative. rove: n 2 is positive. Which of the following is the assumption in the indirect proof? F n is positive. G n 2 is negative. H n is any real number. J n is neither positive nor negative. 170 HSIM14_N_R_M1_M4.indd age 170 27/06/13 8:55 M ehi-6 /129/00739_N/HSIM14_NILLRIS/NILLRY/HSIM14/Math_01//Layout/In...
23. Given: Lines m and n intersect in point. rove: Lines m and n are coplanar. Which of the following could be a statement in the indirect proof? Lines m and n do not intersect in point. Lines m and n are not coplanar with point. Since lines m and n are not in the same plane, they do not share common points. D Since lines m and n do not share common points, they are not coplanar. 24. In a field, Raja, Mary, and Miguel are standing in the shape of a triangle. Raja is 128 feet from Mary, and Mary is 143 feet from Miguel. Which of the following is a possible distance between Raja and Miguel? F 153 feet G 271 feet H 288 feet J 307 feet 25. What is the sum of the measures of the interior angles of the figure below? 26. rcs of congruent circles were constructed from the endpoints of Y, intersecting at points and as shown. What is true about any point on Q T in this construction? F Y will be an acute isosceles triangle. G Y will be an equilateral triangle. H will be on the perpendicular bisector of Y. J will be equidistant from and. 27. Which of the following would prove that quadrilateral QRST is a parallelogram? T Q QR _ ST QR ST Q _ S and T _ R D Two pairs of sides are congruent. S R M N O 28. What is the most specific name for the quadrilateral LD with the coordinates (-3, 1), (0, 5), L(4, 2), D(1,-2)? Q 900 720 540 D 360 F square G parallelogram H rectangle J rhombus 171 HSIM14_N_R_M1_M4.indd age 171 27/06/13 8:55 M ehi-6 /129/00739_N/HSIM14_NILLRIS/NILLRY/HSIM14/Math_01//Layout/In...
29. Which values for x and y will show that MTH is a parallelogram? 33. Find the midpoint of the midsegment of the trapezoid if = (4s, 4t), = (4u, 4t), and = (4v, 0). y x = -6, y = 1 4 x = 4, y = -7 (0, 0) x x = 1, y = 1 D x = 3, y = -2 30. Use the given coordinates to classify the triangle and find its perimeter. S(1, -6), (6, -6), U(3, -2) F acute isosceles; = 15 G acute isosceles; = 10 + 225 H acute scalene; = 10 + 225 J acute scalene; = 15 31. Which of the following statements is NOT true? The diagonals of a rhombus are perpendicular to each other. The diagonals of a kite are perpendicular to each other. The diagonals of a kite bisect each other. D The diagonals of a rhombus bisect each other. (t + u + v, t) (s + u + v, 2t) (u + 2v, 2t) D (2s + 2u, 2t + 2t) 34. The coordinates of three vertices of a parallelogram are (0, 0), (8, 5), and (15, 7). Which of the following is NOT a possible fourth vertex? F ( -7, -2) G ( -3, -8) H (23, 12) J (7, 2) 35. If 6, then which of the following is true? 32. The figure shown is a kite. What is the x-coordinate of point? (a, 1) (a 4, 1) F a 2 + 4 H a + 2 G a + 4 2 J 2a + 4 D m 7 m D 7 = D D m D 7 m STO 172 HSIM14_N_R_M1_M4.indd age 172 27/06/13 8:55 M ehi-6 /129/00739_N/HSIM14_NILLRIS/NILLRY/HSIM14/Math_01//Layout/In...