a ray that divides and angle into two congruent angles triangle a closed polygon with 3 angles whose sum is 180

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1 Geometry/PP Geometry End of Semester Review 2011 Unit 1: Shapes and Patterns asic oncepts Good definitions Inductive reasoning Symbols and terms detailed and use precise words, such as supplementary or adjacent based on known facts or observable patterns the language of geometry used to represent specific terms such as point, line, plane, segment, ray, angle, triangle, perpendicular, congruent, etc. Point, line, and plane point line plane undefined terms on which geometry is based no dimension, no length or width always named with a PITL LETTER contains at least 2 points points on a line are collinear has only 1 dimension, length specific length can not be determined or measured, but the distance between points on the line are measurable contains at least 3 points has two dimensions, length and width (area) specific length and width can not be determined distance between points or lines on the plane can be measured or determined segment ray angle piece of a line with two end points has one dimension specific length can be measured or determined one endpoint and continue in the opposite direction for ever specific length cannot be measured distance between the end point and another point on the line can be measured formed by two rays with a common end point measured in degrees midpoint a point exactly equidistant between two other points on a line divides a line segment into 2 congruent pieces angle bisector a ray that divides and angle into two congruent angles triangle a closed polygon with 3 angles whose sum is 180

2 1. Right angles always measure. 2. Vertical angles are (always, sometimes, never) congruent. 3. Vertical angles are (always, sometimes, never) adjacent to each other.. djacent angles that form a right angle are (always, sometimes, never) complimentary. 5. omplimentary angles are (always, sometimes, never) adjacent to each other. 6. Linear pairs (always, sometimes, never) equal cute angles (always, sometimes, never) measure more than 0 and less than Obtuse angles (always, sometimes, never) measure more than 0 and less than Linear pairs (always, sometimes, never) measure Supplementary (always, sometimes, never) measure If m = 5x - 10, find the value(s) for x that would ensure that was an obtuse angle. Do your work here. 12. If m = 3x - 6, find the value(s) for x that would ensure that was an acute angle. Do your work here. x x 13. If m = x + 2, find the value(s) for x that would ensure that was a right angle. Do your work here. 1. If = 3x - 8 and = x + 12, find the value of x. Do your work here. x x =

3 15. If = x + 1 and = 5x + 20, find the length of. Do your work here. 16. Sketch the following: m = 5, m D = 135, m D = 180. Do your work here x = 17. Use the given information to find the value of x. m O = 8x - 5 m OD = 3x + 5 re and m D complimentary or supplementary? Do the work for #17 here. O D 18. Sketch the following: m = 5, ray bisects D. Determine the m D. Do your work here 19. Sketch the following: is midpoint of seg. Seg DF is the perpendicular bisector of seg. re and m D complimentary or supplementary? 20. Draw line Z. Points T and W are equidistant from. Which segments are congruent? and What is true about seg T and seg W?

4 22. If m = 3x +, m = 2x + 1, and m = x + 13, find the measure of all three angles. 21. Do your work for #22 here. m m m = = = Unit 2: Transformations asic oncepts reflection translation rotation glide reflection exact size and shape of original flipped image, such as looking in a mirror exact size, shape, and direction moved either up, down, left, right exact size and shape image has been turned either clockwise or counterclockwise symmetry occurs when two halves of a figure mirror each other across a line.

dilation original image is either enlarged or reduced reduction original enlargement 1. Rotate the triangle 90 counterclockwise about the origin. (, ) (, ) (, ) 2.

5 dilation original image is either enlarged or reduced reduction original enlargement 1. Rotate the triangle 90 counterclockwise about the origin. (, ) (, ) (, ) 2. Translate the triangle 6 units down. (, ) (, ) (, ) Rotate the triangle 90 clockwise about the origin. (, ) (, ) (, ). Is this a reflection, rotation, translation, or dialtion?

8 6 2-10 -5 5 10-2 - -6 5. Is this a reflection, rotation, translation, or dialtion? 6. Is this a reflection, rotation, translation, or dialtion? 7.

Graph and label the original point and the translated point. 8.

6 Is this a reflection, rotation, translation, or dialtion? 6. Is this a reflection, rotation, translation, or dialtion? 7. What is the image of the point (-8, -12) after a dilation of 1? Graph and label the original point and the translated point. 8. What is the image of the point (-1, 5) after a dilation of 2? Graph and label the original point and the translated point. y x y x

7 Try these: 1. If m = 37 and D is its complement, then what the supplement of? 2. If m XYZ = 2x + 6, and x is the measure of its complement, then what is the measure of the supplement of XYZ? 3. If P is y, then what would be its complement? Write an expression that would represent how to solve.. If Q is represented by W, then what would be its supplement? Write an expression that would represent how to solve. 5. If T is between and Z, T = 2x + 8, Z = x +10, and TZ = 6x 30, then what is the value of x? 6. What is the distance from to? What is the midpoint? X = Z =

a triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles

acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;