2015-2016 Honors Geometry A Review

HONORS GEOMETRY ASemester Exam ReviewHonors Geometry ASemester Exam Review2015-2016

HONORS GEOMETRY ASemester Exam ReviewThe following formulas will be provided in the student examination booklet.Pythagorean TheoremIn right triangle ABC with right angle at point C:a 2 b2 c 2AcbBCaTrigonometryIn a right triangle with acute angle A:sin A side opposite Ahypotenusecos A side adjacent to Ahypotenusetan A side opposite Aside adjacent to AIn any triangle ABC:sin A sin B sin C abcAorabc sin A sin B sin Cc 2 a 2 b 2 2ab cos C The Law of CosinesArea of a triangle MCPS1ab sin C2The Law of SinesBC

HONORS GEOMETRY ASemester Exam ReviewItems on this review are grouped by Unit/TopicUnit 1, Topic 11.Write the three undefined terms in geometry.2.Construct the angle bisector of angle A below.A3.Construct a right angle at point B below.B MCPSCReview Page 1

HONORS GEOMETRY A4.Semester Exam ReviewA road construction crew wishes to construct a new road parallel to the current road, andpassing through the town of Herkimer, marked by point H below. Construct the locationof the road.current roadH5.The perpendicular bisector of AB is constructed. What is true about every point on thatperpendicular bisector?6.The angle bisector of CDE is constructed. What is true about every point on the anglebisector?7.A line is constructed parallel to a given line. What is true about the corresponding pointson the lines? MCPSReview Page 2

HONORS GEOMETRY ASemester Exam ReviewUnit 1, Topic 28.Point A 1, 4 is to be transformed to point A using the translation rule x, y x 3, y 6 . What are the coordinates of point9.A ?Triangle ABC has been transformed to triangle A B C .yACA BOxC B a.State in words, the transformation(s) that produce triangle A B C .b.Write a function rule that represents this transformation.c.Why must ABC A B C ?d.On the coordinate plane above, sketch the reflection of ABC across the x-axis.Label the triangle DEF. Write the function rule for this transformation. MCPSReview Page 3

HONORS GEOMETRY A10.Semester Exam ReviewLet x, y be a point on the coordinate plane. Write the coordinates of the image point if x, y undergoes the following transformations.a.Reflected across the x-axis.b.Reflected across the y-axis.c,Translated six units to the right and two units downward.d.Rotated clockwise 90 degrees about the origin.e.Rotated 180 degrees about the origin.f.Rotated counter-clockwise 90 degrees about the origin.g.Translated two units down, then reflected about the x-axis.h.Reflected across the line x 1 .11.yOADBxCa.Reflect the figure above across the line y 1 . Label the image A B C D .b.Does this transformation preserve lengths and angle measurements? Justifyyour answer.c.If the figure was reflected across the x-axis, then translated two units upward,would the result be the same as the transformation in part a) ? MCPSReview Page 4

HONORS GEOMETRY ASemester Exam Review12.Write the three rigid transformations.13.If a figure undergoes a rigid transformation, then the transformed figure must beto the original figure.14.Look at the figure below.yOxComplete each statement such that each transformation will map the figure onto itself.a.A reflection across the axis or the line x .b.A rotation of degrees about the point . MCPSReview Page 5

HONORS GEOMETRY A15.Semester Exam ReviewTriangle ABC undergoes a transformation to produce triangle A B C . The triangles areshown below.yACBOxB C A a.Can the transformation above be performed using a single reflection? Justify youranswer.b.Can the transformation above be performed by a single translation? Justify youranswer.c.Determine a transformation with three reflections that will produce triangleA B C . MCPSReview Page 6

HONORS GEOMETRY A16.Semester Exam ReviewThe line y 3x 2 is graphed on the coordinate plane below.yOxWrite the equation of the line if y 3x 2 isa.reflected across the x-axis.b.reflected across the y-axis.c.translated three units to the right and one unit up. MCPSReview Page 7

HONORS GEOMETRY ASemester Exam ReviewUnit 1, Topic 317.If figure ABCD is congruent to figure EFGH, complete the congruence statements. A BC 18.If all corresponding sides of two figures are congruent, and all corresponding angles ofthe two figures are congruent, then the figures must be .Items 19 through 23 use the figure below, where point S is the midpoint of WU . ThereforeWS US .RWTSUYou wish to prove WSR UST .19.To prove this congruence by SSS, what two congruence statements are needed in additionto WS US ?20.To prove this congruence by SAS, what two congruence statements are needed inaddition to WS US ?21.To prove this congruence by ASA, what two congruence statements are needed inaddition to WS US ?22.To prove this congruence by AAS, what two congruence statements are needed inaddition to WS US ?23.If RW TU and R T , must RWS be congruent to TUS ? Justify your answer. MCPSReview Page 8

HONORS GEOMETRY A24.Semester Exam ReviewConsuela wants to determine the length of a power line that will be stretched over alake. She cannot walk through the lake. She was able to take some measurements,hoping to determine the length of the power line. Her measurements are shown below.625 ftFigure NOT drawn to scale450 ft500 ft500 ft450 ftPower LineConsuela believes that the length of the power line is 625 feet, but she’s not sure how toexplain this to her boss.Using what you know about triangle congruence, help Consuela by writing a brief reportas to why the length of the power line is 625 feet. MCPSReview Page 9

HONORS GEOMETRY ASemester Exam ReviewIn items 25 through 30 below, information is given about triangles ABC and FED. State whetherthe triangles can be proven congruent by ASA, SSS, AAS, or SAS. If the triangles cannot beproven congruent, state why.EB25.AB FE , AC FD, A F .CA26. A F , B E , C D .CAB FE , AC FD, BC ED .DCD B E , AC FD, BC ED .CADFEB30.FEB29.FEBAFECA28.DB A F , B E , AB FE .FEBA27.D A F , AB FE , C DA MCPSCDFReview Page 10

HONORS GEOMETRY ASemester Exam ReviewUnit 1, Topic 431.Every quadrilateral that is a parallelogram has certain properties. List all theseproperties.32.What properties does a rectangle have in addition to those of a parallelogram?33.What properties does a square have in addition to those of a rectangle?34.Triangle DEF is isosceles with D E . Which sides are congruent?35.In the figure to the right,Figure NOT drawn to scaleD is the midpoint of AB and E is the midpoint of AC .AD 8, BC 22CBThe ratio of AB to AC is 2 to 3.DEDetermine the lengths of EC and DE .A MCPSReview Page 11

HONORS GEOMETRY A36.Semester Exam ReviewIn the figure below, D is the midpoint of AB and E is the midpoint of AC .CBDEAComplete the statements using the items in the box on the right. Each item may be used morethan once or not at all.a.AD b.AE c.is parallel tod.DE is one-half the length ofe.The ratio AB : AD isf.The ratio AE : AC is MCPSADAEDEBCEC2 :1BD1: 2Review Page 12

HONORS GEOMETRY A37.Semester Exam ReviewIf two parallel lines are cut by a transversal:a.Which angle pairs are congruent?b.Which angle pairs are supplementary?p38.Given: m n, 1 161 23 4Prove: p q9 1011 1239.5 68m13 1415n16DC A DAB DE7AGiven:qBEProve: CE CB MCPSReview Page 13

HONORS GEOMETRY A40.Semester Exam ReviewDAGiven:C is the midpoint of BE.AB DCAB BE , DC BEProve: A D41.BECBelow is a figure that will help you prove that the sum of the angles of a triangle is 180degrees. The two lines are parallel.14325mnWrite a proof for this theorem. MCPSReview Page 14

HONORS GEOMETRY ASemester Exam ReviewFigure NOT drawn to scaleUnit 2, Topic 1CB42.In the figure to the right, DE BC .CE 2 AD, AE 8, BD 9, BC 18a.Prove that ADE ABC .DEAb.Determine the length of AD .c.Determine the length of DE . MCPSReview Page 15

HONORS GEOMETRY A43.Semester Exam ReviewJory wants to measure the length, L, of a pond. The figure below shows themeasurements she will use to determine the length of the pond.In the figure below, AE and BD intersect at point C.30 ftABFigure NOT drawn to scale25 ft20 ftC40 ft50 ftDLE ABC EDC ?a.Which similarity postulate/theorem may be used to proveb.What is the length, L, of the pond? Show how you determined your answer. MCPSReview Page 16

HONORS GEOMETRY A44.45.Semester Exam ReviewIf two figures are similar, thena.Corresponding sides are (proportional/congruent).b.Corresponding angles are (proportional/congruent).In the figure below, QRS QTU .SQURTa.Prove that RS TU .b.Complete the proportions.QS SU RTQR RS RT MCPSReview Page 17

HONORS GEOMETRY A46.Semester Exam ReviewThe figure below shows BCD . B C D will be the image of BCD after a dilationwith center B and scale factor 5.Item BankBCBCDComplete the statements using the item bank on the right.D515parallel toa.The point B will be the same point as point .b.C D will be CD .c.The perimeter of B C D will be times the perimeter of BCD . MCPSperpendicular toReview Page 18

HONORS GEOMETRY A47.Semester Exam ReviewOn the graph below, quadrilateral ABCD has been dilated, with the center of dilation theorigin, then translated down six units, to create quadrilateral A B C D .y109876B54B 3A21-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1ODA -11-223456789 10Cx-3-4-5-6-7-8D -9-10C a.What is the scale factor of the dilation?b.What is the ratio of the length of AB to the length of A B ?c.How are the measures of A and A related? MCPSReview Page 19

HONORS GEOMETRY A48.Semester Exam ReviewTriangle ABC is shown on the coordinate grid below.y10987654321-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 OCA123456789 10x-1-2-3-4BP-5-6-7-8-9-10Triangle ABC is to be dilated by a scale factor of three with the center of dilation thepoint P 5, 6 to produce triangle A B C .a.On the coordinate plane above, sketch A B C .b.What is the ratio of the perimeter of ABC to the perimeter of A B C ?c.Is there a sequence of rigid transformations that will produce the same result?Justify your answer. MCPSReview Page 20

HONORS GEOMETRY A49.Semester Exam ReviewQuadrilateral ABCD has been dilated. The dilation results in the quadrilateralA B C D .y10A 9A876DB543D 2C1-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1O-1-212345678B 9 10x-3-4-5-6-7-8-9-10C a.What is the scale factor of the dilation?b.What point is the center of dilation? MCPSReview Page 21

HONORS GEOMETRY A50.Semester Exam ReviewPentagons ABCDE and FGHIJ are similar.B10AC15JGy 1.5IEyDa.What is the value of x?b.What is the value of y? MCPSFigure NOT drawn to scaleF12xHReview Page 22

HONORS GEOMETRY A51.Semester Exam ReviewJack wishes to find the height of a tree. He puts a stick into the ground and uses thetree’s shadow to take some measurements. The figure below shows his measurements.Figure NOT drawn to scaleh ft5 ft135 ft9 fta.Determine the height of the tree.b.Determine the distance from the tip of the tree’s shadow to the top of the tree. MCPSReview Page 23

HONORS GEOMETRY A52.Semester Exam ReviewDraw examples of two triangles that are similar by each similarity postulate/theorem.a.Draw examples of two triangles that are similar by SSS Similarity.b.Draw examples of two triangles that are similar by AA Similarity.c.Draw examples of two triangles that are similar by SAS Similarity. MCPSReview Page 24

HONORS GEOMETRY ASemester Exam ReviewUnit 2, Topic 253.Given right ABC , use the item bank to identify the following. Items may be usedmore than once.ABCItem Bank A B CBCACBCABABBCABACABACACBCBCACABa.Leg opposite Ah.Tangent ratio of Cb.Leg opposite Ci.The angle whose Sine ratio isc.Sine ratio of Aj.The angle whose Tangent Ratio isd.Cosine ratio of Ak.Hypotenusee.Tangent ratio of Af.Sine ratio of Cg.Cosine ratio of C MCPSBCACABBCReview Page 25

HONORS GEOMETRY A54.Semester Exam ReviewLet ABC be a right triangle, with right angle at C.Which statements are true? Check all that apply.A A and B are complementarym A 90o m BBsin Atan A cos A22 AB AC BC C2sin A cos B cos A sin 90o A If A B, then m A 45o55.Look at the two triangles below.1620121220A16BSaundra says that since the two triangles are congruent that sin A sin B . Is Saundracorrect? Justify your answer. MCPSReview Page 26