Test Review Unit 1 Geometry

Geometry Name: 1. Date: ! In the accompanying diagram, transversal RS ! ! intersects parallel lines XY and WZ at E and H, respectively. If mOHEY = 72, what is mOZHS ? 4. 5. 2. ! ! In the accompanying diagram, AGB k CED, mOAGF = 30, and mOCEF = 45. What is mOGFE ? A. 45 B. 52 C. 60 D. 75 ! ! In the accompanying diagram, ABkCD. From ! ! ! point E on AB transversals EF and EG are drawn, ! intersecting CD at H and I, respectively. In the accompanying gure, a k b and c k d. If mO1 = 68, nd mO3. If mO CHF = 20 and mODIG = 60, what is mOHEI? A. 3. Line n intersects lines l and m, forming the angles shown in the diagram below. Which value of x would prove l k m? A. 2.5 B. 4.5 C. 6.25 D. 8.75 page 1 60 B. 80 C. 100 D. 120 6. In the accompanying diagram, mOECB = 6x, mOECD = 3x 11, and mODCB = 74. What is the value of x ? 7. The measures of the three angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of the smallest angle. 8. 9. ^ABC is similar to ^DEF. The ratio of the length of AB to the length of DE is 3 : 1. Which ratio is also equal to 3 : 1? A. mOA mOD B. mO B mOF C. area of ^ABC area of ^DEF D. perimeter of ^ ABC perimeter of ^DEF 12. A. 11. 81 B. 86 C. 108 D. 136 13. In the accompanying diagram of rhombus ABCD, diagonal AC is drawn. If mOCAB = 35 nd mOADC. 14. In parallelogram ABCD, diagonals AC and DB intersect at E. Which statement is always true? As shown in the diagram below, CD is a median of ^ABC . Which statement is always true? 10. In quadrilateral ABCD, mOA = 72, mOB = 94, and mOC = 113. What is mOD? A. AD = DB B. C. OACD = OCDB D. OBCD = OACD AC = AD rectangle B. C. rhombus D. parallelogram 15. a rectangle B. a rhombus C. a square B. Triangle ABD is a right triangle. C. Triangle AEB is congruent to triangle AED. If the perimeter of a square is 8, which is the length of a diagonal? A. trapezoid 16. If the diagonals of a parallelogram are perpendicular but not congruent, then the parallelogram is A. Triangle AED is isosceles. D. Triangle ABC is congruent to triangle CDA. In which quadrilateral are the diagonals always congruent? A. A. B. p 2 3 C. p 8 2 D. 4 The perimeter of a rhombus is 60. If the length of its longer diagonal measures 24, the length of the shorter diagonal is A. 17. p 2 2 9 B. 15 C. 18 D. 20 In rectangle ABCD, diagonal AC = x + 10 and diagonal BD = 2x 30. Find the value of x. D. an isosceles trapezoid page 2 Geometry 18. Two adjacent sides of a rhombus are represented by 5x + 7 and 6x 1. Find the value of x. 19. In the accompanying diagram of rectangle ABCD, mOBAC = 3x + 4 and mOACD = x + 28. 22. In the accompanying diagram, BAE, CAD, OB and OE are right angles, AB = 3, BC = 4, and AD = 15. What is the length of DE ? A. 5 B. 8 C. 9 D. 12 What is mOCAD ? A. 20. B. 37 C. 40 23. D. 50 Triangle ABC is shown in the diagram below. The lengths of the sides of a triangle are 8, 15, and 17. If the longest side of a similar triangle is 51, what is the length of the shortest side? A. 21. 12 32 B. 24 C. 16 D. 4 In the accompanying diagram, ^ABC is similar to ^DEF, OA = OD, and OB = OE. If AB = 3, BC = 12, DE = x + 2, and EF = 18, nd the value of x. If DE joins the midpoints of ADC and AEB, which statement is not true? 24. 1 CB 2 A. DE = C. AD DE = DC CB B. DE k CB D. ^ABC ^AED In the diagram below of right triangle ABC, altitude CD is drawn to hypotenuse AB . If AD = 3 and DB = 12, what is the length of altitude CD ? A. page 3 6 B. p 6 5 C. 3 p D. 3 5 Geometry 25. On level ground, a person 6 feet tall casts a shadow of 8 feet. At the same time, a nearby tree casts a shadow of 20 feet. Find the number of feet in the height of the tree. 26. In the accompanying diagram, ^ ABC is similar to ^PQR, AC = 6, AB = BC = 12, and PR = 8. Find the perimeter of ^PQR. 31. 32. 27. If ^ RST ^ ABC, mOA = x2 8x, mOC = 4x and mOR = 5x + 30, nd mOC. 28. In the accompanying diagram, trapezoid ABCD is similar to trapezoid AFGH. If AF = 18, AB = 54, and HG = 9, what is the length of DC ? In the accompanying diagram of ^ABC, ^ DEF is formed by joining the midpoints of the sides of ^ABC. If DE = 9, FE = 18, and DF = 13, what is the perimeter of ^ABC ? A. 10 B. 20 C. 40 D. 80 In ^ABC shown below, P is the centroid and BF = 18. 5, What is the length of BP? A. 29. In ^ABC, AB = 8, BC = 10, and CA = 16. If D is the midpoint of AB and E is the midpoint of BC, nd the length of DE. 30. In the accompanying diagram of ^ABD, AB ? AD and EC ? AD. If AB = 6, EC = 4, and ED = 8, nd AE. B. 9 C. 3 D. 12 33. In the accompanying diagram, ^ABC is a right triangle and CD is the altitude to hypotenuse AB. If AD = 4 and DB = 16, nd the length of CD. 34. The length of the line segment connecting (2; 2) and ( 3; 1) is A. page 4 6 p 10 B. 2 C. p 26 D. p 34 Geometry 35. In triangles ABC and DEF, AB = 4, AC = 5, DE = 8, DF = 10, and O A = OD. Which method could be used to prove ^ ABC ^DEF? A. 36. AA B. SAS C. SSS 37. D. ASA The measures of two complementary angles are represented by (3x + 15) and (2x 10). What is the value of x? A. 17 B. 19 C. 35 D. 37 Lines m and n intersect at point A. Line k is perpendicular to both lines m and n at point A. Which statement must be true? A. Lines m, n, and k are in the same plane. B. Lines m and n are in two di erent planes. C. Lines m and n are perpendicular to each other. D. Line k is perpendicular to the plane containing lines m and n. page 5 Geometry