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Name _____________________ Geometry Semester 1 Review Guide 1 2014-2015 1. _______ Jen and Beth are Hints: (transformation unit) graphing triangles on this coordinate grid. Beth graphed her triangle as shown. Jen must now graph the reflection of Bethβs triangle over the x-axis. A. B. C. D. 2. _______ The pentagon shown is regular (transformation unit) and has rotational symmetry. What is the angle of rotation? Angle of rotation: A. 45° B. 72° C. 90° 360 π D. 60° How many lines of reflection are there?___ where n is number of sides Number of lines of reflection = n 3. _________ Trapezoid πππΌπ is drawn on the coordinate grid. (transformation unit)If the reflection If you reflect the trapezoid over the dashed line, what would line is diagonal, count on the diagonal! be the new coordinates of trapezoid ? A. Sβ (-1, -6) Wβ (5, 0) Iβ (1, 1) Mβ (-2, -2) B. Sβ (-4, -3) Wβ (2, 3) Iβ (3, -2) Mβ (0, -5) C. Sβ (1, -6) Wβ (-5, 0) Iβ (5, -3) Mβ (2, -6) D. Sβ (3, 5) Wβ (-4, 9) Iβ (-3, 5) Mβ (-6, 2) 4. _________ Find the new coordinates of βπππ» when it is rotated 90° clockwise about the origin. A. Mβ (-6, 1) Qβ (-2, 1) Hβ (-4, 5) B. Mβ (6, -1) Qβ (2, -1) Hβ (4, -5) C. Mβ (5, 4) Qβ (-1, 6) Hβ (-2, 1) D. Mβ (8, 7) Qβ (8, 3) Hβ (5, 4) (transformation unit) Re-plot on a bigger graph! 5. __________ (transformation unit) *Assume the rotation is counterclockwise unless otherwise stated. Μ Μ Μ Μ A. π»πΊ Angle of rotation = 360 π where n is number of sides. B. Μ Μ Μ Μ ππ How many turns is in a 270° rotation? Μ Μ C. Μ Μ ππ Where will EI end up if you turn the Μ Μ Μ Μ D. πΊπ» figure that many counterclockwise? 6. ________ (transformation unit)Angle of rotation = 360 π where n is number of sides. How many turns is in a 240° rotation? Where will X end up if you turn the figure that many counterclockwise? 7. _________ Which of the following is not a rigid (transformation unit) A rigid transformation? transformation occurs when the preimage and the image are congruent. A rigid transformation A. Reflection C. Translation B. Rotation D. Dilation preserves: ο· Distance (lengths of sides are the same ο· Angle measure (angles are congruent) ο· Shape (parallel sides remain parallel, shape does not change) 8. ________ Will the rotation of a pair of parallel lines always result in another pair of parallel lines? A. yes, they will remain parallel to each other through any rotation B. Only if the lines are rotated 180° or 360° C. No, they will always result in intersecting lines D. Bo, they will always result in perpendicular lines (transformation unit) A rotation is an example of a rigid transformation! 9. _________ Square ABCD, shown at the right, is translated up 3 units and right 2 units to (transformation unit) A translation is an example of a rigid transformation!! produce rectangle AβBβCβDβ. Which statement is true? A Μ Μ Μ Μ π΄π΅ β₯ Μ Μ Μ Μ Μ Μ π΄β²π΅β² and Μ Μ Μ Μ π΅πΆ β₯ Μ Μ Μ Μ Μ Μ π΅β²πΆβ² B Μ Μ Μ Μ Μ Μ and π΅πΆ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ β₯ π΄β²π΅β² Μ Μ Μ Μ β₯ π΅β²πΆβ² π΄π΅ C 2π΄π΅ = π΄β²π΅β² and 3π΅πΆ = π΅β²πΆβ² D π΄π΅ + 2 = π΄β²π΅β² and π΅πΆ + 3 = π΅β²πΆβ² (transformation unit) The line y = 2 is a 10. __________What would be the image point Bο’ after a reflection over the line y = 2 and a translation 4 units right and 2 units down? y A. (1, 4) B. (11, -4) C. (1, -4) D. (1, 0) horizontal line through 2 on the y-axis. 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 B -3 -4 -5 -6 x 12. ___________ Steve created this design for a wall mural. (transformation unit) Choose one of the three vertices in figure 1, and count to find its corresponding vertex in image 2. Which describes the translation from figure 1 to figure 2? A. up 3 units and right 1 unit units B. down 1 unit and left 3 units units C. up 4 units and right 4 D. down 4 units and left 4 13. _________Given: Quadrilateral ABCD on this graph. Which graph shows the reflection of ABCD over line l? A. C. B. D. (transformation unit) Use patty paper (transformation unit) Example of dilation: 14. ________ Which description MOST accurately describes a dilation? A. When a shape is dilated, the parallel lines remain parallel B. When a shape is dilated, the angles within the shape change C. When a shape is dilated, the orientation of the shape changes D. When a shape is dilated, the distance between the lines stays the same. 15. __________ Mary Ann drew two lines on the chalkboard. Her two lines lie in the same plane but share no common points. Which could be a description of Mary Annβs drawing? A. A set of skew lines C. A set of adjacent rays B. A set of parallel lines D. A set of collinear points 16. _________ Lines the and are parallel. The , and (Language of Geometry) (Language of Geometry) . Which statement explains why you can use the equation to solve for ? Corresponding example: β 1 & β 5 A. Alternate Exterior Angles are congruent Alternate Interior example: β 3 & β 6 B. Alternate Interior Angles are congruent Alternate Exterior example: β 1 & β 8 C. Complementary Angles are congruent D. Corresponding Angles are congruent 17. _________ Greg used a compass and straight edge to draw the construction below. (Triangles) Vocab: Concurrent: meet at a point Which of these is shown by this construction? Median: line from the vertex of a triangle to midpoint of opposite side Altitide: line starting from the vertex of a triangle and creating a right angle with the opposite side (height) Angle bisector: line that divides an A. The medians of a triangle are concurrent angle into two congruent parts B. The altitudes of a triangle are concurrent C. The angle bisectors of a triangle are concurrent D. The perpendicular bisectors of a triangle are concurrent Perpendicular bisector: line that may or may not start at the vertex, but goes to the midpoint of the opposite side at a right angle. 18. ____________ A segment has endpoints (-4, 8) and (3, -2). What are the coordinates of the midpoint? ( A. (-3.5, 6) C. (-0.5, 3) B. (-1, 6) D. (-1.5, 3) 19. _____________ line Q is perpendicular to the line for the equation: y=- xβ4 What is the slope of line Q? B. - C. 2 3 (Language of Geometry) Perpendicular lines have opposite 2 3 2 π₯+π₯ π¦+π¦ , ) 2 2 Parallel lines have the same slope. 3 A. (Language of Geometry) D. 3 2 2 3 reciprocal slopes. 20. ________ (Quadrilaterals) Points P, Q, and R are shown below. If these points are all vertices of a parallelogram then which point would represent the coordinates of the fourth vertex of parallelogram PRQS. In a parallelogram, opposide sides are A (4,6) B (8,-1) C (5,2) D (9,1) P parallel. Use slope to help find the last point. R Q 21. ___________ What is the coordinate of the midpoint of Μ Μ Μ Μ π΄π΅ ? (Language of Geometry) Where is the middle of -4 and 2? A. -2 B. -1 C. 3 D. 6 22. __________ Which of the following is unneccessary to prove (Triangles) Isosceles triangles: that the 2 base angles of an isosceles triangle are congruent? A. The angle sum theorem for triangles B. SAS postulate C. The definition of angle bisector D. The definition of congruent triangles 23. __________ What is the perimeter of the triangle? (Language of Geometry) A. 18 Perimeter = add up all sides B. 20 Use pythagorean theorem to find the C. 52 side lengths. D. 134 24. __________ Square EFGH is shown below. A dilation of 2 centered at (2,2) is performed. The resulting square is labeled EβFβGβHβ. What is the length of Μ Μ Μ Μ Μ πΉβ²πΊβ² ? A. 2 units B. 3 units C. 5 units D. 6 units (Transformatons) The center is the fixed point. The other vertices will be twice as far from (2, 2) 25. __________ Which of the following is necessary to prove (πππππππππ ) β 3 is exterior angle. β 1 and that a trianglesβs exterior angle equals the sum of the two β 2 are remote interior angles? remote A. the definition of complementary angles interior angles B. The definition of angle bisector C. The definition of supplementary angles D. The definition of congruent triangles 26. _________ A segment connects the midpoints on two sides of a triangle. What is true about this segment (the midsegment)? (Triangles ) Μ Μ Μ Μ Μ π·πΈ is a midsegment 1 Μ Μ Μ Μ π·πΈ = Μ Μ Μ Μ π΅πΆ 2 A. it is always horizontal and half the length of each side. B. It is always perpendicular to the two sides it joins and forms an isosceles triangle with the portions of the sides above it. C. It is always parallel to the third side and half the as long as the third side. D. It is always half the length of those two sides and parallel to the third. 27. _________ When proving the exterior angle sum theorem, (Triangles) The polygon exterior angle the first step is to show that an exterior angle of a polygon and theorem: the sum of the exterior angles an interior angle of a polyhon add together to equal 180°. of any polygon = 360 Which angle classification justifies this step? A. Vertical angles B. Corresponding angles C. Complementary angles D. Linear Pairs of angles 28. __________ and π are the midpoints of ππ and ππ, respectively. (Triangles) Μ Μ Μ Μ is the midsegment! See #26 π π What does the midpoint theorem tell us Μ Μ Μ Μ and ππ Μ Μ Μ Μ ? about the relationship between π π Μ Μ Μ Μ is ½ the length of ππ Μ Μ Μ Μ A. π π Μ Μ Μ Μ is twice the length of ππ Μ Μ Μ Μ B. π π Μ Μ Μ Μ and ππ Μ Μ Μ Μ are not related by that theorem C. π π Μ Μ Μ Μ and ππ Μ Μ Μ Μ are equal in length D. π π 29. __________ Which diagram shows a triangle drawn so that it is congruent to A. B. C. D. ? (Triangles) Congruent means equal in size/measure. Use patty paper if necessary. 30. __________ In the diagram below, what is the measure of β πΈ if the triangles βπ΄π΅πΆand βπ·πΈπΉ are similar? (Triangles) **In similar triangles, corresponding angles are congruent! A. 30° B. 60° C. 90° D. 70° 31. ____________ Triangle is rotated to become triangle . Without the use of any measurement devices, which could be used to prove that triangle is congruent to triangle ? A. SAS beause both are right triangles, JK is congruent to JβKβ and KL is congruent to KβLβ B. ASA because both are right triangles and JL is congruent to JβLβ C. SAS because both are right triangles, JL is congruent to JβLβ and JK is congruent to KβLβ (Triangles) You must have 3 pairs of congruent angles and sides to use ASA or SAS. The sides and angles must be corresponding!! Try highlighting the information in the multiple choices to see if the sides and angles correspond. D. ASA because both are right triangles and angle J is congruent to angle Lβ and JK is conguent to KβLβ 32. _________ Triangle is rotated, reflected, and translated to yield triangle Be careful on the order of the sides and . angles! Which statement proves that the two triangles are congruent? A. and is taken to is taken to , B. is taken to , and is taken to , is taken to , and is taken to is taken to , is taken to , and is taken to C. . D. . (Triangles) . is taken to . 33. ___________ Which of the triangles below is similar to ΞXYZ? (Triangles) In similar figures, sides are proportional. Write pairs of corresponding sides as fractions and simplify. If they all reduce to the same number, this is the similarity ratio. If they do nt all reduce to the same number, the triangles are not similar. Be careful when you write the A. C. corresponding sides as fractions β be consistant on which triangle is the numerator and which is the denominator! B. D. all of the above (Triangles) 34. _________ Which statement correctly completes the sentence below? There is no AAA congruence theorem! If two distinct pairs of angles in two triangles are congruent, then _________ A. The pair of included sides must also be congruent and the triangles must be congruent B. The pair of included sides must also be congruent and the triangles must be similar cont on next page C. The third pair of angles must also be congruent and the triangles must be congruent D. The third pair of angles must also be congruent and the triangles must be similar. 35. ________ The dotted lines in the figure below show how Jenny inscribed circle in right triangle on a practice test. What should Jenny have done differently to answer the question correctly? A. Jenny could have used the (Triangles) Vocab: ο· the polygon ο· B. Jenny should have constructed an inscribed circle. Circle O is circumscribed. Circumcircle/circumscribed circle: around the polygon ο· altitudes of the triangle to find the incenter. Incircle/inscribed circle: inside Medians are concurrent at centroid ο· Angle bisectors are concurrent at incenter ο· Perpendicular bisectors are concurrent at circumcenter C. Jenny should have used the bisectors of angles X, Y, and Z to find the incenter. ο· Altitudes are concurrent at orthocenter D. Jenny should have put points A, B, and C at the midpoints of the triangle. 36. _________ Solve for x and y: A. x = 99 y = 74 B. x = 74 y = 99 (Quadrilaterals) If a quadrilateral is inscribed in a circle, then opposite angles are supplementary: C. x = 81 y = 106 D. x = 106 y = 81 37. ____________ True or false: If a figure is a parallelogram then it is a rectnagle. 38. __________ Which of the following quadrilaterals DOES (Quadrilaterals) NOT have perpendicular diagonals? A. rhombus B. square C. kite D. parallelogram 39. __________ Which of the following have congruent (Quadrilaterals) diagonals? Draw the figures A. rectangle, rhombus, square B. rectangle, square, isosceles trapezoid C. kite, parallelogram, trapezoid D. parallelogram, rectangle, rhombus, square 40. ___________ What are the coordinates of G? (Quadrilaterals) A. (2a, b) B. (-2a, -b) C. (2a, -b) D. (-2a, b) A. left 8 down 12 (Transformations) β©π₯, π¦βͺ X is the horizontal slide B. right 8 down 12 Y is the vertical slide 41. _________ The translation vector β©β8, 12βͺ means to go: C. left 8 up 12 D. right 8 up 12 42. _________ What is the line of reflection? A. x = -2 (Transformations) Hoy Vux Horizontal lines are of the form B. x βaxis y=k C. y = -2 x=h D. y- axis Vertical lines are of the form 43. ________Which is the correct list of undefined terms in (Language of Geometry) geometry? A. point, line, ray B. point, line, plane C. segment, angle, point D. plane, helicopter, jet 44. _________ Line A passes through (-3, 5) and (1, -3). (Language of Geometry) Parallel lines have What is the slope of the line that is parallel to line A? the same slope. A. 2 Perpendicular lines have opposite reciprocal C. -2 slopes. Graph the points and count B. 1 2 D. - 1 2 formula πππ π ππ’π or use the π¦2 βπ¦1 π₯2 βπ₯1 45. _________ Line A passes through (2, 5) and (-1, 1). What (Language of Geometry) Parallel lines have is the slope of the line that is perpendicular to line A? the same slope. A. 4 3 C. - B. 3 4 D. - Perpendicular lines have opposite reciprocal 4 3 slopes. 3 4 Graph the points and count formula π¦2 βπ¦1 π₯2 βπ₯1 πππ π ππ’π or use the