Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Regular polytope wikipedia , lookup
Coxeter notation wikipedia , lookup
Euler angles wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Mirror symmetry (string theory) wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Multilateration wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Tessellation wikipedia , lookup
Complex polytope wikipedia , lookup
Event symmetry wikipedia , lookup
Geometry Unit 1 Review (sections 6.1 – 6.7) 1A, B: Slope, Distance, Parallel and Perpendicular A 1. Find the slope of AB. 2. Find the slope of a line that is perpendicular to AB. B 3. Find the distance between A and B (the length of AB. ) 4. Write the equation of the line that is the perpendicular bisector of AB. 1C: Performing Transformations Using the diagram above to match the Image/Pre-Image listed on the left with the transformation listed on the right. Shape II Shape I 5. Pre-image: Shape I Image: Shape II a. Rotated 180° around the point (0 , 0) 6. Pre-image: Shape II Image: Shape III b. Reflected over the line 𝑦 = −𝑥 7. Pre-image: Shape IV Image: Shape II c. Rotated 270° counterclockwise around the point (0 , 0) 8. Pre-image: Shape I Image: Shape IV Shape IV Shape III 9. Pre-image: Shape I Image: Shape III Perform the requested transformations. Make sure to label A' and B’. 10. Reflect over the line y = -2. d. Reflected over the line 𝑦=0 e. Rotated 90° counterclockwise around the point (0 , 0) 11. Rotate 180° around the point (-1 , 2). A B A B 12. Reflect over the line 𝑦 = 𝑥. 13. Draw the line of reflection that maps P onto P’. Then write its equation. A B 15. 14. C D B A A' B' D' C' K J K' I I' J' 1E: Rotational and Line Symmetry in Polygons 16. How many total diagonals are there on the regular polygon to the left? 17. How many lines of symmetry are there on the shape to the left? 18. List all of the degrees of rotational symmetry for the shape to the left. 19. Is there any pattern between the number of sides of a polygon and the number of diagonals it has? Explain or give an example. 1F: Quadrilaterals and their properties 20. Sketch and label rectangle ABCD in the space below. Then mark your picture to indicate the property that OPPOSITE SIDES ARE Parallel. 21. Sketch a quadrilateral whose diagonals are perpendicular. MARK YOUR PICTURE to indicate this property. Then give the most specific name of the figure. 22. The rhombus has 2 lines of symmetry that are also the diagonals of the figure. EXPLAIN how a line of symmetry helps prove that the DIAGONALS OF A RHOMBUS BISECT EACH OTHER.. 23. Sketch and label parallelogram ABCD in the space below. Then mark your picture to indicate the property that OPPOSITE ANGLES ARE CONGRUENT. 24. Which of the following statements are TRUE about the square? Circle all that apply. 25. List the name(s) of all quadrilaterals that share both of the following characteristics. Diagonals are congruent. Opposite sides are parallel. Opposite angles are congruent. The square is a rectangle. 26. The graph below shows the diagonal of a square. Locate the other two vertices of the square. Then use slope to verify that the figure has 4 right angles. Opposite sides are parallel. The diagonals bisect the opposite angles. Then support your reasoning using symmetry of the figure. 27. Three vertices of a parallelogram are given below. Identify the fourth vertex. Then use slopes and distance to verify that the opposite sides of a parallelogram and congruent and parallel.