Geometry Semester 1 Final Review Part 1 (Units 1 3)

Transcription

1 Name: Date: Block: Geometry Semester 1 Final Review Part 1 (Units 1 3) Unit 1 (Holt Sections ) 1. Draw and label each of the following. a) a line containing points R and S. b) a ray with endpoint B that passes through L. c) a plane containing a segment with endpoints X and Y. 2. Use the diagram at right to name each of the following. a) three collinear points b) a plane containing T, X, and Y. c) two segments d) a line containing Q and T. 3. Use the diagram at right to find the length of each segment. a) MP b) NQ 4. T is between R and V. RV = 31 and VT = 14. Find RT.

2 5. Use the diagram at right to find AB. 6. M is the midpoint of AB. AM = 11x 9 and BM = 7x a) Find the value of x. b) Find AM. c) Find BM. 7. Name all of the angles in the diagram at right. 8. Classify each angle measure by its measure. a) m XYZ = 90 b) m PQR = 17 c) m BRZ = bisects LMP, m LMT = (4x 13), and m TMP = (2x + 17). Find m LMP.

3 10. Use the diagram at right to determine whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. a) 2 and 3 b) 1 and 5 c) 3 and Find the perimeter and area of each figure. perimeter: area: _ perimeter: area: _ c) d) perimeter: area: _ perimeter: area: _

4 12. Find the coordinates of the midpoint of HJ with endpoints H(-7, -4), and J(3, -2). 13. S is the midpoint of RT, R has coordinates (-5, 1) and S has coordinates of (-1, 4). Find the coordinates of T. 14. Use the diagram at right to find LM and NP to the nearest tenth. Then determine if. Unit 2 (Holt Sections , and CPM Sections , 1.2.5) 15. Find the coordinates for the image of figure JKLM after the translation (x, y) (x +2, y 2). Graph the image. J (, ) L (, ) K (, ) M (, ) 16. A figure has vertices X(-5, 4), Y(-2, 0), and Z(-5, -4). After a transformation, the image has vertices at X (5, 4), Y (2, 0), and Z (5, -4). Sketch the preimage and image and identify the transformation. Transformation:

5 17. Describe each transformation as a reflection, translation, rotation, glide reflection, or none of these. c) d) e) f) 18. Draw the reflection of the figure across the line. 19. a) Graph the quadrilateral with vertices A(-3, 4), B(-5, -2), C(-2, -5), D(0, 2). b) Translate ABCD along the vector. Label the image A B C D and list the coordinates of the vertices of the image. A(-3, 4) A (, ) B(-5, -2) B (, ) C(-2, -5) C (, ) D(0, 2) D (, ) c) The rule for transforming any point under this translation is: (x, y) (x, y )

6 20. a) Translate ABCD along and then reflect the image across line t. b) The transformation above is called a because ABCD is translated and then reflected across a line that is to the vector. 21. Rotate the figure with the given vertices about the origin using the given angle of rotation. a) A(2, 0), B(5, -2), C(7, 1); 90 counterclockwise. Label the image A B C and list the coordinates of the vertices of the image. A(2, 0) A (, ) B(5, -2) B (, ) C(7, 1) C (, ) The rule for transforming any point under this rotation is: (x, y) (, ) b) J(1, 1), K(4, 3), L(3, 6); 180. Label the image J K L and list the coordinates of the vertices of the image. J(1, 1) J (, ) K(4, 3) K (, ) L(3, 6) L (, ) The rule for transforming any point under this rotation is: (x, y) (, )

7 22. State whether each figure has line symmetry. If so, draw all lines of symmetry. c) d) 23. State whether each figure has rotational symmetry. If so, find the angle of rotational symmetry and the order of symmetry. angle: order: angle: order: c) d) angle: order: angle: order:

8 24. Use the diagram at right to give an example of each angle pair. a) same-side interior angles b) alternate exterior angles c) corresponding angles d) linear pair e) alternate interior angles f) vertical angles 25. Use the diagram at right to find the value of x. List the postulate or theorem used. 26. For each diagram, find the value of x. Then find each angle measure. 27. Write the equation of the line through (-3, -1) and (3, -3) in slope-intercept form.

9 28. Write the equation of the line through (6, -2) with slope 3 4 in point-slope form. 29. Write the equation of the line with y-intercept -3 through the point (2, 5) in pointslope form. 30. Write the equation of the line with x-intercept -4 and y-intercept 2 in slope-intercept form. 31. Graph each pair of lines and use their slopes to determine if they are parallel, perpendicular, coincident, or neither. a) AB and CD for A(-1, 0), B(1, 5), b) LM and NP for L(-3, 2), M(-1, 5), C(4, 5), D(-2, 4) N(2, 3), P(1, -5)!## " c) PR and QS for P(2, -1), Q(0, 0), R(-4, 2), S(-2, 1)!#" d) GH and FJ for F(-3, 2), G(-2, 5), H(2, 4), J(2, 1)

10 32. Graph each line. a) y = 3x 1 b) y 1 = 3 (x + 2) 5 c) y = -5 d) x = Write the equation of each line. 34. Write the equation of the perpendicular bisector for each segment. a) AB with A(2, 6) and B(-8, 4) b) with R(-5, 1) and S(6, -8)