Honors Geometry Semester 1 Final Test Supplement REVIEW

Name: Date: Hour:Honors Geometry – Semester 1 Final Test Supplement REVIEWDirections: Complete each of the following. Fill in blanks and show work when algebra is involved.Chapter 1 – Essentials of Geometry1.Let B be the midpoint between A and C on AC .Find AB and AC.AB 7x – 9BC 2x 21x 2.AB AC Given m ABC 75 and the following are true, then find m ABD and m DBC .m ABD 3x – 6A m DBC 4x 11D x m ABD m DBC 3. CB If ray QS bisects PQR and the following are true, then find m PQS and m PQR .m PQS 9x – 21P m SQR x 35x Q m PQS m PQR 4.S RFind the values of x and y for the given diagram.(7 x 11) (2 x 20) 2y x y 5. Given the endpoint R(–3, –2) and midpoint M(–1, –8) of RS , find the coordinates of the other endpoint.6. Given the endpoint R(–2, 5) and midpoint M(–1, 3) on RS , find the coordinates of the other endpoint S.HGeo S1 Final Supplement Test REVIEW 1-20161

7. The endpoints of LF are L( 2,2) and F (3,1) . The endpoints of JR are J (1, 1) and R(2, 3) .What is the approximate difference in the lengths of the two segments? Are the two segments congruent?8. m A is 42º greater than m B . If A and B are supplementary, find m A and m B .Write an equation.9. Two angles form a linear pair. The measure of one angle is 8 times the measure of the otherangle. Find the measure of each angle.Write an equation.Chapter 2 – Logic and Reason10. Use the diagram at the right to find x, y and the measure of each angle.Given: m 1 2(5 x 5) m 3 (6 x 50) m 4 5( y 1) 142311. Write an equation and find the value of x and the measure of each angle for the figure below.5x 6(x – 2) 7(2x 6) Chapter 3 – Parallel and Perpendicular Lines12. Given that lines l, m, and n are parallel. Find the values of x, y, and z.(4y – 9) 73 lx (3x 26) my z z n13. Write the equation of the line that passes through point P (2,3) and has the slope of m HGeo S1 Final Supplement Test REVIEW 1-20161.42

14. Write an equation of line m passing through the point (8, –3) that is perpendicular toline n with the equation y 4 x 5 .a) GRAPH line n.b) Write the slope-intercept equation of line mc) GRAPH line m.d) State a conjecture for:Lines m and n are perpendicular lines.15. Write an equation of the line p passing through the point (4, 5) that is parallel to the line q with theequation 3x 4 y 12 . State the equation and graph the lines p and q.16. Write an equation of the line p passing through the point (4, 0) that is perpendicular to the line q with theequation 12 x 3 y 9. State the equation and graph the lines p and q.17. Graph the equation 2 x 3 y 18 and state the x-intercept and the y-intercept.HGeo S1 Final Supplement Test REVIEW 1-20163

18. Complete each of the following.a. Plot the points A(1, 4) and C ( 3,4) . b. Slope of AC :c. y-intercept of AC : d. Write an equation of AC in slope-intercept form.e. Find AC. f. Plot P(2,4) . Find the distance from P(2,4) to line AC .g. Write an equation in slope-intercept form for the line containing P(2,4) and the distance intersection point on line AC .Chapter 4 Congruent TrianglesDirections: For problems 19 – 27, write a two-column proof to prove the following.* Please mark the picture, number steps and reasons, and clearly write the reasons.A19. Given: AB // DC A CProve: AD BCB1243CD20.Given: ABC is an Isosceles triangle with legs AB and ACAD bisects BACProve: ABD ACDABHGeo S1 Final Supplement Test REVIEW 1-2016CD4

21.Given: RT bisects QUQRRS STProve: QSR USTST22.Given: XW XZ , VZ XZXY YZProve: WXY VZYUVXYZW23.XGiven: XY ZYXZ WYProve: XYW ZYW VYWZ24.AGiven: AB EC , AD DED is the midpoint of BCProve: ABD ECDB25.EDCCGiven: ACB and ADB are right anglesCB DBProve: ACB ADBAHGeo S1 Final Supplement Test REVIEW 1-2016BD5

E26.Given: ET bisects BER and BTRProve: BET RETRBT27.Given: AB ACBD DCProve: ABD ACDABDC28. Find the value of x and the specified angles. Show your work.x Bm A 2x m B (103 – x) (6x – 7) CA m BCD D29. Find the value of x and y. Show your work.3 y x (x 2) y (4 x 10) HGeo S1 Final Supplement Test REVIEW 1-20166

30. Given: ABC with the vertices A(–5 , 0), B(0, 5), and C(0, 0) and DEF with the vertices D(5, 0), E(0, 5), and F(0, 0).a. Graph the two given triangles.b. Algebraically prove that ABC DEF .c. Algebraically determine if ABC & DEFare right triangles.d. Classify the two given triangles bytheir side lengths.AB DE BC EF AC DF Slope of AB Slope of DE Slope of BC Slope of EF Slope of AC Slope of DF ABC Sides Classification: DEF Sides Classification:Is ABC a Right Triangle? Yes or NoIs DEF a Right Triangle? Yes or NoBased on your Algebraic proof, explain why ABC DEF :HGeo S1 Final Supplement Test REVIEW 1-20167

Chapter 5 – Relationships within Triangles31. Graph ABC with vertices A(0,0) , B ( p, q ) , and C (2 p,0) .Find the length and the slope of each side.Then find the coordinates of each midpoint. Is ABC an isosceles triangle? Is it a right triangle?(Assume all variables are positive and p q .)a. AB BC AC b. Is ABC an Isosceles triangle? Explain.c. slope of AB :slope of BC :slope of AC :d. Is ABC a Right triangle? Explain.e. midpoint, M, of AB : midpoint, N, of BC :f. Construct MN on the graph above of ABC .i. What type of special triangle segment is MN .32. Graph ABC . Find the length and the slope of each side. Then find the coordinates of eachmidpoint. Is ABC a right triangle? Is it isosceles? Explain.Label the midpoints of BC and AC J and K. Is JK a midsegment? Justify why or why not.A(2m,0) , B(0,2n) , and C (2m,2n) (Assume variables are positive and m n )HGeo S1 Final Supplement Test REVIEW 1-20168

33. Graph ABC . Find the length and the slope of each side.(10)Is ABC a right triangle? Justify your answer.Classify ABC by its sides. Justify your answer.A(0,0) , B(m,0) , and C (0, n) (Assume variables are positive and m n )34. Graph ABC with the vertices A( 8,2) , B(4,8) , and C (4, 4) .a) Find the balancing point of ABC and label it DCoordinates of D:(2)b) Find the coordinates of each midpoint of ABC and labelthem J, K, L. Connect each midpoint of ABC .Are JK , KL , and LJ midsegments? Pick one segmentand justify why or why not. Refer to the slope and lengthof the segment.(8)HGeo S1 Final Supplement Test REVIEW 1-20169

Directions: Write a two-column proof to prove the following.* Please mark the picture, number steps and reasons, and clearly write the reasons.Given: ABC is an Isosceles triangle with vertex AAD is the median to base BCProve: ABD ACD35.ABDC36. Is it possible to construct a triangle with the following side lengths? If not explain.a. 34, 42, 8b. 25, 16, 3737. Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.10 feet, 37 feetChapter 6 - Similarity38. ABC RST . Find x, y, z, and the scale factor from ABC to RST .Ax 50 y R2012y-4z xScale Factor:zCBTS161239. If ABC EFD , then find the value of x, y, and the perimeter of EFD .x Ay E610y (2x – 4) C60 B8DF4Perimeter of EFD HGeo S1 Final Supplement Test REVIEW 1-201610

Determine whether each pair of triangles is similar.40.Possible Reasons: AA , SSS , SAS JQSimilar?5Yes orNo4Similarity Statement if similar:89 89 KRL10P841.If so, how?YB25Similar?17.51620CZ20If so, how?1442.NoSimilarity Statement if similar:XAYes orIf BE // CD in ACD, then find BE, AD, and ED.State the similarity statement: ACD How are the two triangles similar?AA ,SAS ,orSSS (Circle one)A18BE 24BAD E15ED CD55Find the value of x. * not to scale.43.1116.5x2920 z2144.1620 z21x2836HGeo S1 Final Supplement Test REVIEW 1-201611

Write a two-column proof to prove the following.C45.Given: AB// CDProve: ABE DCEAEB46.RXSX XT XUProve: RXS TXUDGiven:URXSTF47.Given: U and M are right anglesProve: FUN OMNMNUO48.Given: BE // CDProve: BAE CADABECDHGeo S1 Final Supplement Test REVIEW 1-201612

Honors Geometry – Semester 1 Final Test Supplement REVIEW Directions: Complete each of the following. Fill in blanks and show work when algebra is involved. Chapter 1 – Essentials of Geometry 1. Let B be the midpoint between A and C on AC. Find AB and AC. AB 7x – 9 BC 2x 21 x _ AB _ AC _ 2. Given m ABC 75