* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry Final Exam Review #1 Name: Period: Find the measure of
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
Multilateration wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Line (geometry) wikipedia , lookup
Euler angles wikipedia , lookup
Golden ratio wikipedia , lookup
Lie sphere geometry wikipedia , lookup
Apollonian network wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euclidean geometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Transcript
Geometry Final Exam Review #1 Name: Period: Find the measure of the unknown angle. 1. m CFD = ______________ 2. m BFC = ______________ 3. m AFD = ______________ 4. m BFE= ________________ Find the measure of the angle. 5. m AOB ______________ 6. m DOE _____________ 7. m EOF _____________ 8. m BOF _____________ Complete the statement with corresponding, alternate interior, alternate exterior, or consecutive interior angles. 9. 1 and 6 are __________________________ 10. 4 and 8 are __________________________ 11. 2 and 5 are __________________________ 12. 3 and 8 are __________________________ Find the measure of the numbered angles. 13. 14. In the diagram, JKL MNO. Complete the statement. 15. N _____________ 16. JK = ______________ 17. m K = ____________ State the conjecture used to prove the triangles are congruent. 18. 19. Complete the statement using DEF where L, M and N are midpoints of each side. 20. LN || _____________ 21. MN || ____________ 22. If DF = 26, then LM = ___________ 23. If EM = 10, then LN = ___________ 24. If perimeter of DEF = 60, then perimeter of LMN = _____________ Name the shortest and longest side of the triangle. 25. 26. 27. 28. 29. Determine if the measures can form the sides of a triangle. a. 70, 79, 18 b. 72, 5, 77 c. 14, 90, 25 30. Given 2 sides of triangle, between what 2 numbers must the measure of 3rd side fall. a. 37 and 16 b. 5 and 23 c. 41 and 28 31. What is the longest side in the figure. L F 25 89 82 43 73 48 T A 32. What is the longest side in the figure. I 60 T 33. 56 34 76 64 R 70 E Classify the triangle below by its angles and sides. 50 40 34. Classify the triangle below by its angles and sides. 98 41 35. In ABC, mA = mB = mC, classify the triangle by its angles and sides. 36. In isosceles triangle, GHI, I is the vertex angle and mG = 72. Find mI. 37. In the figure below, mABD = (7x + 9), mD = (6x), and mC = (42 – 2x). Find x. A B C D 38. Complete the congruence statement, ABC ___________ by ____________. B D C A 39. E Complete the congruence statement, ABC ___________ by ____________. B A D C Complete the congruence statement if ADC is an isosceles triangle with vertex angle, D, and AE CB . ABC ___________ by ____________ and BA EC by ____________ 40. B E D A C 41. ABCD is a parallelogram. mB = (13x + 27), mC = 49. Find x. 42. If EFGH is a parallelogram, complete each statement. F G a) FEH ______________ b) FG = _________________ c) FJ = __________________ J E d) HEG ______________ H e) mGFE + ______________ = 180 43. ABC is a triangle with three midsegments. A 4 D Perimeter of ABC _________ Perimeter of DEF _________ E 3 B F 7 44. a. Fill in the blank. C z ________x b. Fill in the blank. x_______9 A 13 7 9 zº D B xº 11 C 53º 49º 7 x 45. Write the correct notation and the inverse, converse and contrapositive of the statement below. If I ride on the Ferris wheel, then I am not afraid of heights. a. Inverse ( ): b. Converse ( c. Contrapositive ( ): ): 46. Write the equation of the line (in slope intercept form) that passes through the given point and parallel/perpendicular to the given line. a. (8, -3); parallel to y= x – 7 3 4 b. 2 3 (-12, 3); perpendicular to y= x + 4 47. a. To construct a circumscribed circle, you must locate the __________________________. b. To construct an inscribed circle, you must locate the _____________________________. c. What are the 4 triangle congruence shortcuts?__________________________________. d. What do you call lines that are NOT in the same plane and do not intersect? __________ 48. STAR is a square with diagonals that intersect at M. a. mSAT = ____________ b. mRMS = ___________ Helpful Review for Points of Concurrency: CENTROID Intersection of 3 medians. Always lies inside the triangle. Divides the median into 2 segments where the longer segment is twice the length of the shorter segment. The center of gravity or balancing point of any triangle. ORTHOCENTER CIRCUMCENTER Intersection of 3 perpendicular bisectors. May lie outside the triangle (obtuse triangle). May lie on the triangle (right triangle). May lie inside the triangle (acute triangle). Point is equidistant from all of the angles. The point is the center of the circumscribed circle (see below). Intersection of 3 altitudes. May lie outside the triangle (obtuse triangle). May lie on the triangle (right triangle). May lie inside the triangle (acute triangle). INCENTER Inscribed and Circumscribed Circles Intersection of 3 angle bisectors Always lies inside the circle Point is equidistant from all the sides of the triangle (perp distance). The point is the center of the inscribed circle (see below). Equilateral Triangle All 4 points of concurrency meet at the same point in an equilateral traingle.