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Transcript
Geometry Review for 2015 Fall Semester Exam Name:_____________________________________________ Hr:____ Read each question carefully. 1) Randy is proving that in parallelograms opposite angles arecongruent. He is using the fact that when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent. Which pair of statements establishes that there is a pair of opposite congruent angles in the parallelogram? A) Angles 3 and 6 are congruent. Angles 5 and 6 are congruent. B) Angles 1 and 6 are congruent. Angles 5 and 7 are congruent. C) Angles 2 and 5 are congruent. Angles 5 and 7 are congruent. D) Angles 1 and 6 are congruent. Angles 6 and 3 are congruent. 2) What are two undefined terms that are useful for defining asegment? A) angle, line B) line, point C) point, ray D) ray, distance 1 3) If Figure 1 is reflected across the y-axis and rotated 90° counterclockwise around point C, which statement is true? A) The area increases by a factor of 2. B) The area decreases by a factor of 2 . C) The area stays the same. D) The area increases by 2 the length of the base times the height. 1 1 _________________________________________________________________________________________ 4) 5) What is demonstrated by the construction? A) a line through R parallel to line l B) a line through R congruent to line l C) a line through R perpendicular to line l D) a line through R bisecting line l Which best completes the definition below? Parallel lines: two or more lines on a plane that A) have one point of intersection B) have no points of intersection C) are horizontal D) are vertical 2 6) Which figure shows the shape below rotated 90° clockwise about the origin? A) Figure 1 B) Figure 2 C) Figure 3 D) Figure 4 ___________________________________________________________________________________________ 7) Which of the following could be proven? A) ∠ADE ≅ ∠EDC B) ∠EDC ≅ ∠FDB C) m∠EDF = 90° D) ∠ADE ≅ ∠BDF ______________________________________________________________________________________ 8) What is demonstrated by this construction? A) parallel lines B) perpendicular lines C) perpendicular bisector D) angle bisector 3 9) The vertices of a regular hexagon inscribed in a circle are numbered 1 through 6 in order. Point 1 is selected as a vertex for an equilateral triangle to be inscribed into the circle. Which point will make another vertex of the triangle? A) a point of intersection of the circle and the perpendicular bisector of the segment with endpoints 2 and 3 B) a point of intersection of the circle and the perpendicular bisector of the segment with endpoints 3 and 4 C) point 5 _______________________________________________________________________________________ 10) What is demonstrated by this construction? A) intersecting lines B) congruent angles C) angle bisector D) complementary angles __________________________________________________________________________________________ 11) A series of rigid motions superimposed Quadrilateral 1 onto Quadrilateral 2. The side lengths of Quadrilateral 1 listed clockwiseare 7, 7, 8, and 9. Which is a possible list of the side lengths of Quadrilateral 2, in clockwise order? A) 7, 8, 7, 9 B) 7, 9, 7, 8 C) 8, 7, 9, 7 D) 8, 7, 7, 9 4 12) 13) Which triangle was constructed congruent to the given triangle? A) Triangle 1 B) Triangle 2 C) Triangle 3 D) Triangle 4 What is described below? All the points on a line located between points A and B, including points A and B. A) ray AB B) segment AB C) a line that is parallel to line AB D) a line that intersects line AB ___________________________________________________________________________________________ 14) Which of the following could be proven? A) B) C) D) ∠1 ≅ ∠2 m∠5 + m∠2 = m∠7 ∠3 ≅ ∠4 m∠4 + m∠1 = m∠5 + m∠6 5 15) Which transformation maps the solid figure onto the dashed figure? A) reflection across the x-axis B) reflection across the y-axis C) translation to the left D) rotation about the origin 16) A) B) C) D) 61° 60° 59° 58° __________________________________________________________________________________________ 17) Which transformation maps the solid figure onto the dashedfigure? A) reflection across the x-axis B) reflection across the y-axis C) rotation about the origin D) translation down 6 18) Based on the side length relationships of triangles ABC and XYZ,which statement is true? AB = XY AC = ZY BC = ZX A) The information provided is not sufficient to decide whether the triangles are congruent. B) The triangles are congruent. C) The triangles are not congruent. _________________________________________________________________________________________ 19) The following is known about triangles ABC and DEF: AB = DE BC = EF CA = FD After a series of rigid transformations is applied to triangle DEF, the image of side DE coincides with side AB of triangle ABC. If D'E'F', the image of triangle DEF, does NOT coincide with triangle ABC, which of the following statements is true? A) A reflection of the triangle D'E'F' across line AB must coincide with triangle ABC. B) A reflection of the triangle D'E'F' across the perpendicular bisector of segment AB must coincide with triangle ABC. C) Two reflections may be necessary to have the image of triangle D'E'F' coincide with triangle ABC. 20) Which best completes the explanation of the SAS criterion for triangle congruence? If two pairs of corresponding sides and the of pair corresponding included angles are congruent, ... A) then the triangles are congruent regardless of whether other pairs of corresponding parts are congruent. B) then one triangle can be made to coincide with the other by applying a dilation. C) then there are two more pairs of congruent corresponding angles, and the remaining pair of sides are also congruent. 7 21) If triangle ABC is rotated 90° clockwise about point B, what are the new coordinates of point A? A) (-3, 3) B) (3, 3) C) (3, -3) D) (-3, -3) 22) The following is known about triangles ABC and DEF: ∠A ≅ ∠D AB = DE CA = FD After a series of rigid transformations is applied to triangle ABC, the image of angle A coincides with angle D. Which of the following about B'C', the image of segment BC, is true? A) Segment B'C' must coincide with EF. B) Segment B'C' may or may not coincide with EF. B'C' = EF. C) Segment B'C' may or may not coincide with EF. B'C' may or may not be equal to EF. ________________________________________________________________________________________ 23) If triangle ABC is rotated 90° clockwise about point C, what are the new coordinates of point A? A) (4, 4) B) (5, 4) C) (4, 3) D) (3, 4) 8 24) The expressions for two angles from two different triangles aregiven. For which value of x could the two triangles be congruent? Triangle 1 angle measures: (x+10)°,(x + 20) Triangle 2 angle measures: (2x 10)°,(2x - 30)° A) 20 B) 30 C) 40 D) 50 25) If triangle ABC is rotated 90° clockwise about point A, what are the new coordinates of point B? A) (-5, -1) B) (-1, 5) C) (-5, 1) D) (1, -5) 26) Which rigid motion could be used to show that triangle ABC is congruent to triangle DEC? A) a rotation B) a translation C) a reflection 9