GSE GeometryUnit 1 - TransformationsName:Vocabulary: Translations, Dilations, Reflections, Rotations, and Isometric.1) Translate the following points bythe rule: x,yx 1,y - 42) Translation: (x, y)(x – 2, y – 6)EOC ReviewBlock:3) Reflection over y xW(3, 2) C(2, 4) T(3, 5) Z(5,2)S (-5, 2)Y (-4, 5)R (-1, 1)A (-4, -2)4) Reflection over y -35) Rotate the figure 90 CW6) Rotate the figure 90 CCW7) Find the coordinates of the newvertices of the image that has beendilated by a factor of 5.8) Find the coordinates of the newvertices of the image that has beendilated by a factor of 1/2.9) Draw a dilation with k 2S(-5, 2)W(3, 2)Y (-4, 5)C(2, 4)R (-1, 1)T (3, 5)A (-4, -2)Z (5, 2)10) Determine the scale factor, k 11) Given the pointsM (-3, 1) S (5, -2)Translate: (x – 3, y 2)Reflect: y x12) Given the pointsK (0, -4) P (-6, -3)Reflect: over the x-axisRotate: 270 CCWK’K’’M’M’’S’S’’R (1, 2)P’P’’R’R’’
GSE GeometryUnit 1 - TransformationsEOC ReviewAnswers1) Which transformation maps the solid figureonto the dashed figure?A.B.C.D.rotation 180 about the origintranslation to the right and downreflection across the x-axisreflection across the y-axis2) If triangle ABC is rotated 180 degrees aboutthe origin, what are the coordinates of A’?A.B.C.D.2)(-5,-4)(-5,4)(-4,5)(-4,-5)3) Determine the angle of rotation for A to maponto A’?A.B.C.D.1)3)45901351804) Which transformation will place the trapezoidonto itself?A. counterclockwise rotation about the originby 90B. rotation about the origin by 180C. reflection across the x-axisD. reflection across the y-axis4)
GSE GeometryUnit 1 - TransformationsEOC Review5) 𝐽𝐾𝐿 is rotated 90 about the origin and then translated using (𝑥, 𝑦) (𝑥 8, 𝑦 5). What are thecoordiantes of the final image of L? The coordinates for 𝐽𝐾𝐿 are J(5,-1), K(4,4), and 6) Which figure has 90 rotational symmetry?6)A.B.C.D.squareregular hexagonregular pentagonequilateral triangle7) Point P is located at (4,8) on a coordinate plane. Point P will be relfected over y x. What will beethe coordiantes of the image of point P?A.B.C.D.(28,4)24,8)(4,28)(8,4)8) Point F’ is the image when point F is reflected over the line 𝑥 2 and then over the line 𝑦 3. Thelocation of F’ is (3,7). Which of the following is the location of point F?A.B.C.D.9)A relfection over the x-axisA relfection over the y-axisA rotation 99 clockwiseA rotation 90 counterclockwise10) The vertices of 𝐽𝐾𝐿 have coordinates J(5,1), K(-2,-3), and L(-4,1). Under which tranformation is theimage 𝐽′𝐾′𝐿′ NOT congrunet to 𝐽𝐾𝐿?A.B.C.D.8)(-7,-1)(-7,7)(1,5)(1,7)9) A triangle has vertices at A(-3,-1), B(-6,-5), C(-1,-4). Which tranformation would produce an imagewith vertices A’(3,-1), B’(6,-5), C’(1,-4)?A.B.C.D.7)A translation of two units to the right and two units downA counterclockwise rotation of 180 degrees aound the originA reflection over the x-axisA dilation with a scale factor of 2 centered at the origin10)
GSE GeometryUnit 2 – Triangles and QuadrilateralsEOC ReviewName:Block:Vocabulary: Supplementary, complementary, vertical, same side interior, same side exterior,alternate interior, alternate exterior, corresponding, triangle, quadrilateral, and parallelogram.1) Name the angles listed and thespecial property.1 and54 and62 and84 and52) Given m n and m 8, find themeasures of all the numbered anglesin the figure.m 1 m 2 m 3 m 4 m 5 m 6 m 7 m 8 1123) Solve for x.4) Solve for x.5) Solve for x.6) solve for x.7) Solve for x.8) Solve for 𝑥 𝑎𝑛𝑑 𝑚 𝐽JM9. Solve for x.10) Find x and y.11) Find x and y.120K
GSE GeometryUnit 2 – Triangles and QuadrilateralsEOC ReviewAnswers1) Peach Street and Cherry Street are parallel. Apple Street intersects them, as shown in the diagrambelow. If 𝑚 1 2𝑥 36 and 𝑚 2 7𝑥 9, wjat is 𝑚 1?A.B.C.D.1)91754702) What is the measure of 𝐵 in the figure below?2)A.B.C.D.625859563) In this figure, l m. Jessie listed the first two steps in a proof that 1 2 3 180𝑜 . Whichjustification can Jessie give for step 1 and 2?A.B.C.D.Alternate interior angles are congruent.Corresponding anlges are congruent.Vertical angles are congruent.Alternate exterior angles are congruent.4) In the diagram below of parallelogram STUV, 𝑆𝑉 𝑥 3, 𝑉𝑈 2𝑥 1, 𝑎𝑛𝑑 𝑇𝑈 4𝑥 3. What is the̅̅̅̅ ?length of 𝑆𝑉A.B.C.D.3)24574)
GSE GeometryUnit 2 – Triangles and QuadrilateralsEOC Review5) In parallelogram ABCD, find m A.5)A.B.C.D.15 70 110 200 6) What reason explains why the m Q 115 ?6)A)B)C)D)diagonals of a parallelogram bisect each otheropposite sides of a parallelogram are congruentopposite angles of a parallelogram are congruentconsecutive angles of a parallelogram are supplementary7) Find x and y in the diagram.7)A)B)C)D)x 60, y 30x 45, y 60x 30, y 60x 60, y 1208) List the angles of the triangle in order from SMALLEST to LARGEST.8)A)B)C)D) C, B, A A, B, C C, A, B B, C, A
GSE GeometryUnit 2 – Similarity, Congruence, and ProofsEOC ReviewName:Block:Vocabulary: SSS, SAS, ASA, AAS, HL, CPCTC, Reflexive Property, Definition of a Midpoint, Midsegment.Determine if the following triangles are similar. (SSS, AA, SAS, None)1 ABC by2) GHI by3)MNO by4) Solve for x.5) Solve for x.6) If a 42.9 ft tall flagpole casts a253.1 ft long shadow, then how longis the shadow that a 6.2 ft. tall womancasts?7) Solve for x.8) Solve for x.9) Solve for x.Determine if the following triangles are congruent. (SSS, SAS, ASA, AAS, HL, None)10)11)12)13) Given: ABDCProve:1. ABDC1.2. ACAC2.ABC& CDACDA14) Given: RTReasonsStatements3.ABCTV, STTUStatements1.RT2.2. Given3.3.RTSVTU4.4.RTSVTU4.5.5.TSRTUV5.3.are right angles.4.ABC5.ABCCDACDATSRReasons1.TVProve:TUV
GSE GeometryUnit 2 – Similarity, Congruence, and ProofsEOC ReviewAnswers1) Use this triangle to answer the question.2) Look at the triangle.1)2)This is a proof of the statement “If a line is parallel toone side of a triangle and intersecrts the other twosides at distinct points, then it seperates these sidesinto segments of proportional lengths.”Which triangle is similar to the given triangle?Which reason justifies step 2?A.B.C.D.Alternate interior angles are congruent.Alternate exterior agnler are congruent.Corresponding angles are congruent.Vertical angles are congruent.3) Which can be used to prove the triangles arecongrunet?4) In the triangle shown, GH DF.3)4)A.B.C.D.SSSASASASAASWhat is the legnth of GE?A.B.C.D.2.04.57.58.0
GSE GeometryUnit 2 – Similarity, Congruence, and Proofs5) In the disgram, CD is the perpendicular disector ofAB. The two-column proof shows that AC iscongruent to BC.EOC Review6) In the triangles shown, 𝐴𝐵𝐶 is dilated by a2factor of to form 𝑋𝑌𝑍.5)36)Given that 𝑚 𝐴 50𝑜 𝑎𝑛𝑑 𝑚 𝐵 100𝑜 , what is𝑚 𝑍?A.B.C.D.15253050Which of the following would justify step 6?A. ASSB. ASAC. SASD. SSS7. Given the diagram below, what is the value of x?7)A.B.C.D.13.514.615.516.68. To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20 feet from the baseof the mappost. She then stepped back 4 feet so that she could see thee top of the lamppost in the centerof the mrror. Rachel’s eyes are 5 feet and 6 inches above the ground. What is the height, in feet, of thelamppost?8)
GSE GeometryUnit 3 – Right TrianglesName:Vocabulary: Sine, cosine, tangent, complementsEOC ReviewBlock:5) 𝑠𝑖𝑛75𝑜 𝑐𝑜𝑠1) Find sin A 2) Find tan B 6) 𝑐𝑜𝑠40𝑜 𝑠𝑖𝑛3) Find cos B 7) 𝑐𝑜𝑠540 𝑐𝑜𝑠4) Find tan A 8) Find f.9) Find m.10) Find x.432585f7m11) Find angle P.12) Find s.32p4013) Solve for theta.13s14) From 25 feet away from the base of a building, theangle of elevation from the ground to the top of a buildingis measured to be 38 . How tall is the building?1715) A kite is 35 feet in the air and the string forms anangle of 62 with the ground. How long is the string?
GSE GeometryUnit 3 – Right TrianglesEOC ReviewAnswers1) A 30-foot long escalator forms a 41 angle at the second floor. Which is the closestheight of the first floor?A.B.C.D.1)20 feet22.5 feet24.5 feet26 feet2) The diagram below shows a ramp connecting the ground to a loading platform 4.5feet above the ground. The ramp measures 11.75 feet from the ground to the top of theloading platform. Find the angle of elevation.2)3) What is the sine ratio of 𝑃 in the given triangle?3)A.B.817815C.15D.151784) Which is equal to sin 30 ?4)A.B.C.D.cos 30 cos 60 sin 60 sin 70
GSE GeometryUnit 3 – Right TrianglesEOC Review5) A rope is tied to the bottom of a hot air balloon as shown below. The rope makes anangle of 35 with the ground and is 75 ft. long. How far is the bottom of the balloon from5)the ground to the nearest foot?A.B.C.D.43 ft.53 ft.61 ft.131 ft.6) The captain of a submarine views an iceberg from his periscope, as shown in thefigure below. What is the height of the iceberg to the nearest meter?A.B.C.D.161 m192 m210 m298 m7) Jeff lives on Oak Street, and Tom lives on Main Street. How much farther, to thenearest yard, is it for Tom to walk down Main Street and turn on Oak StreetA.B.C.D.6)46 yd48 yd126 yd172 yd7)
GSE GeometryUnit 4 – Circles, Angles, and AreaName:Vocabulary: Sine, cosine, tangent, complementsEOC ReviewBlock:1) Find m GHJ2) Find mCD3) Find m C4) Find m 1 and m 25) Find 1 & 26) Find 1.7) Find 1 & 2.8) Find the area of a circle with adiameter of 22 inches.9) The circumference of a circle is25.12 ft. What is the radius?10) Find the arc length of AB11) Find the area of the shaded region12) If the radius of the circle is 6centimeters, what is the area of theshaded segment?
GSE GeometryEOC ReviewAnswers1) An insulated foam sleeve is made to fit over water pipe. The distance from the centerof the water pipe to the edge of the sleeve is 6 inches. The hole in the center has a1)radius of 3 inches. What is the area of the face of the foam sleeve?A.B.C.D.Unit 4 – Circles, Angles, and Area9.42 𝑖𝑛218.84 𝑖𝑛284.78 𝑖𝑛2141.30 𝑖𝑛22) This circle, with center point Q, has a radius of 10 centimeters. The length of theminor arc NP is 20.42 centimerters. To the nearest degree, what is the value of x?A.B.C.D.2)110𝑜117𝑜204𝑜233𝑜3) Find the area of the shaded sector of circle O.3)A.B.C.D.5𝜋20𝜋25𝜋50𝜋4) What is the area of the shaded part of the circle?4)A.B.C.D.57𝜋 𝑐𝑚24135840585138𝜋 𝑐𝑚2𝜋 𝑐𝑚2𝜋 𝑐𝑚2
GSE GeometryUnit 4 – Circles, Angles, and Area5) What is the measure of 𝐴𝐵𝐶?EOC Review5)A.B.C.D.15𝑜30𝑜60𝑜120𝑜6) In this circle, AB is tangent to the circle at point B, AC is tangetnt to the circle at pointC, and point D lies on the circle. What is the 𝒎 𝑩𝑨𝑪?̂ is 800 . What is the value of x?7) The measure of 𝐶𝐷A.B.C.D.504035256)7)
GSE GeometryUnit 4 – Segment Lengths and VolumeEOC ReviewName:Block:Vocabulary: Chord, tangent, volume, chevalier’s principal, Pythagorean Theorem, cross section.1) Find the value of x.2) Find the value of x.3) Find the value of x.4) Find the value of x.5) Is AB a tangent? Why or whynot?6) Find the value of x.7) Find the volume of the figure witha diameter of 12 in and a height of20 in.8) Find the volume of the hemisphere.9) If10) Find the Volume of a squarebased pyramid.11) Name the cross sectionthe volume of a cone is 23𝑖𝑛 , what is the volume of acylinder with the same basearea and height? Explain howyou got to youranswer?312) Name the cross section
GSE GeometryUnit 4 – Segment Lengths and Volume1) What is the volume of a cylinder with a radius of 3 in. and a height ofA.B.C.D.81227427894EOC ReviewAnswers92in.?𝜋 𝑖𝑛3𝜋 𝑖𝑛3𝜋 𝑖𝑛3𝜋 𝑖𝑛32) A cereal box is 10.4 inches high, 7.4 inches long, and 2.3 inches wide. What is thevolume of the cereal box rounded to the nearest cubic inch?A.B.C.D.2)771401772363) Frances bought a new refrigerator to replace her old refrigerator shown below. Hernew refrigerator has the same length and width as the old refrigerator but is 8 incheshigher. How many more cubic inches of space are in Frances’s new refrigeratorcompared to her old refrigerator?A.B.C.D.1)8,64014,88017,85625,4403)
GSE GeometryUnit 4 – Segment Lengths and VolumeEOC Review4) The grain bin below is made up of a cylinder with a cone on top. To the nearest cubicfoot, how much grain will this bin hold?4)A.B.C.D.5,625 𝑐𝑢𝑏𝑖𝑐 𝑓𝑒𝑒𝑡17,663 𝑐𝑢𝑏𝑖𝑐 𝑓𝑒𝑒𝑡32,987 𝑐𝑢𝑏𝑖𝑐 𝑓𝑒𝑒𝑡70,650 𝑐𝑢𝑏𝑖𝑐 𝑓𝑒𝑒𝑡5) A square pyramid is packaged inside a box. The space inside the box around thepyramid is then filled with protective foam. About how many cubic inches of foam isneeded to fill the space around the pyramid?A.B.C.D.5)8 cubic inches41 cubic inches83 cubic inches125 cubic inches6) In circle P below, DG is tangent. 𝐴𝐹 8, 𝐸𝐹 6. 𝐵𝐹 4, and 𝐸𝐺 8. Find ̅̅̅̅𝐶𝐹̅̅̅̅and 𝐷𝐺 .̅̅̅̅ 𝐶𝐹̅̅̅̅ 𝐷𝐺
GSE GeometryUnit 5 – Geometric and Algebraic ConnectionsName:Vocabulary: Midpoint, distance, partition, endpoint, circle1) Write the equation of the circle instandard form2) Find the midpoint of(5, 1) and (6, 7).EOC ReviewBlock:3) Find the coordinates of the otherendpoint of a segment with anendpoint of (-2, 2) and amidpoint (8, 3).4) Brandy and Mandy are in the pool playing a game ofMarco Polo. Brandy swims 10 ft south and 7 ft east ofbase. Mandy swims 6 ft north and 5 ft west from wherethey started together in the middle of the pool. How farapart are Brandy and Mandy?5) Determine whether Point A (-5, 8) lies on the circlewhose center is Point C (1, 2) and which contains thePoint P (7, -4).6) Find the area and perimeter of the figure.7) Given that a parallelogram’s sides are parallel, provethe following is a parallelogram.8) Write an equation of the line that passes through(-3, 4) and is parallel toY -3x – 1.9) Write an equation of the line that passes through (5, -3)and is perpendicular to y -5/2x 1.10) Find a point P on the segment with endpoints A(-1, -3)and B(7, 1) that partitions it in a 3:1 ratio.11) Find a point T on the segment with endpoints C(-4, -6)and D(2, 3) that partitions it in a 2:1 ratio.
GSE GeometryUnit 5 – Geometric and Algebraic Connections1) A circular sidewalk is beingconstructed