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SEMESTER 1 FINAL EXAM REVIEW 1A - 1B - MODE SCORES 1C 3A 3B - STANDARD HOMEWORK 1A Date: Questions: 1B Date: Questions: 1C Date: Questions: 3A Date: Questions: 3B Date: Questions: 4A - 4B - Standard 1A 1. Given B is between A and C, AB = 7 and AC = 17. Determine BC. BC= 2. Given ∠𝐴 and ∠𝐷 are complemetary angles and m∠A = 63 ° . Determine 𝑚∠D. 𝑚∠D= 3. Given ∠𝐸 and ∠𝐹 are supplementary angles and 𝑚∠𝐹 = 72°. Determine 𝑚∠E. 𝑚∠E= 4. Given SP bisects ∠TSQ with m∠TSP = 64° , determine m∠TSQ . P Q T S m∠TSQ = 5. Given m∠ADB = 70°, m∠ADC = 100° , determine m∠CDB . B A 1 2 C D m∠CDB = 6. Given lines a || b, 𝑚∠4 = 102° determine 𝑚∠6. 1 2 3 4 a 5 6 7 8 b m∠6= 7. Given the diagram, determine x. 55˚ 31˚ x˚ x= Given parallelogram ABCD, m∠A = 46° , determine m ∠ B and m∠C. 8. A B D C m∠ B = 9. m∠C = Given ABCD is a rhombus, 𝑚∠2 = 21°. Determine the measure of the remaining angles. A B 2 1 4 3 D C m∠1 = m∠3 = m∠4 = 10. Given HJML is a rectangle, 𝑚∠3 = 100°. Determine the measure of the remaining angles. H J 2 3 L 1 M m∠1 = m∠2 = 11. Given A is between B and C, BC = 20 and AC = 4. Determine AB. AB= 12. Given m∠P = 40°, determine the measure of its complement. 13. Given m ∠ ABD = 40 ° and m ∠ DBC = 80 ° , determine m ∠ DBC. D A C B m ∠ DBC= 14. Given the diagram, determine y. y˚ 40˚ y= 15. Given the diagram and m ∠ 1 = 60 ° , determine the measure of the following angles. 1 p 3 5 4 2 m∠2 = q m∠3 = m∠4 = m∠5= 16. Given line l is parallel to line m, m∠2 = 72° , determine m∠3 . l m . 1 2 3 4 p m∠3 = 17. Given the triangle is an isosceles triangle and the base angle 55°, determine the measure of the vertex angle. Vertex Angle= 18. Given PQRS is a parallelogram, and 𝑚∠𝑃 = 125°, determine the measures of 𝑚∠S and 𝑚∠R. Q R P S 𝑚∠S= 𝑚∠R= Standard 1B 1. Given G is the midpoint of CJ , CG = 2x - 2 and GJ = 3x – 7. Determine x and CJ. x= CJ= 2. Given G bisects AC , AC = 4x – 2 and GC = 4x - 9. Determine GC. GC= 3. Given FH bisects ∠EFG and m∠EFG = (10x + 6)° and m∠HFG = (2x + 21)° , determine m∠EFH . E H G F m∠EFH = 4. Given m∠1 = (2x − 7)° and m∠2 = (7x + 7)° , determine the m∠1 . 2 1 m∠1 = 5. Given the diagram, m∠1 = (13x − 7)° and m∠2 = (15x − 13)° , find m∠1 and m∠3 . 3 1 2 m∠1 = m∠3 = 6. Given 𝐴𝐵 ⊥ 𝐶𝐷 , 𝑚∠1 = (𝑥 + 2)° and 𝑚∠2 = (2𝑥 + 7)°, determine x and 𝑚∠2. A E 1 C 2 D B x= m∠2= 7. Given Δ TCA is isosceles with base CA , AC = 3x, AT = 3x − 2, TC = 2x + 5 . Determine the length of the base. Length as Base: 8. Given ΔBUZ ≅ ΔTON , UZ = 10x – 70, ON = 5x, and TO = 2x + 46. Determine BU. BU= 9. Given l m , determine x and m∠1 . l (15 + x)˚ 1 (2x)˚ m x= m∠1 = 10. Given CY is an altitude of ΔACB . If 𝐴𝑌 = 4𝑥 + 5, 𝐴𝐵 = 3𝑥 − 10, and 𝑚∠𝐶𝑌𝐵 = 5𝑥 − 10 °, determine AB. C A Y B AB= 11. Given ABCD is a rectangle, AC = 4x – 60, BC = 18 and BD = 30 – x. Determine AE. A B E D C AE= 12. Given TP is a base of a trapezoid TRAP, 𝑚∠𝑇 = (15𝑥 + 2)° , 𝑚∠𝑅 = (2𝑥 + 8)°, and 𝑚∠𝑃 = (10𝑥 + 17)°, determine the value of x. x= 13. If 𝑚∠1 = (10𝑥 − 10)° and 𝑚∠2 = (5𝑥 + 30)°, determine x and 𝑚∠3. 1 3 2 x= m∠3= 14. Given 𝑙 ∥ 𝑚, determine x and 𝑚∠1. l (6x)˚ (8x - 40)˚ m 1 m∠1 = x= 15. Given ∆MNP is isosceles and MP is the base, m∠N= (5x + 4)° and m∠P = (4x + 10)°. Determine m∠ M. m∠M= 16. Given QT is a median of ΔBPT , BT = 2x + 5, TP = 5x – 13, BQ = 3x + 4, QP = 8x – 11. Determine BP. B Q T P BP= 17. Given JK is the altitude of ΔJAC . Determine x and CA. J (8x+2)° 5x - 2 C 2x + 10 K x= A CA= 18. Given, ΔABC ≅ ΔDEF, AB = 15, BC = 20, DF = 2x + 7, and FE = 3x – 7. Determine x and AC. x= AC = 19. Given TRAC is a parallelogram, TK = 2x + 7 and TA = 6x + 6. Determine KA. T R K C A KA= 20. Given ABCD is a rectangle, AR = 7x − 3 and BD = 16x − 12 . Determine AC. B A R C D AC= 21. Given ABCD is a rhombus, m∠3 = 5x + 8 and m∠4 = 3x + 16 determine m∠2. A B 2 1 3 D 4 C m∠2= Standard 1C 1. Given the number line, determine the coordinate of the midpoint of CT . A C B P S T -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2. Determine the coordinates of midpoint of JP if J(3, 8) and P(7, -16). 3. Determine the exact distance from A(-7, 9) and K(-2, 0). AK= ! 4. Write the equation of a line, in point-slope form, that is perpendicular to 𝑦 + 2 = ! (𝑥 − 1) and passes through the point (7, -3). 5. Determine the slope of the line parallel to the line containing (-1, 5) and (5, 3) 6. Given pre-image point A (5, -3) is rotated 90˚ counterclockwise about the origin. Determine the coordinates of the final image A 7. Given pre-image point A(4 , -5). Translate up 3 units and left 2 units, and then reflect A’ over the xaxis. Graph and list the coordinates of A’ and A”. A’ A” A 8. Given ∆HQR with H(-4, 2), Q(-2, 6) and R(4, 4). a. Draw the median HG . b. Write the equation of the line that contains the median HG . Q (-2, 6) (4, 4) R (-4, 2) H __________________________ 9. Determine the coordinates of midpoint of GH if G(6, 10) and P(2, -2). 10. Determine the exact distance from B(4, 6) and L(3, 2). BL= 11. Determine the slope of a line perpendicular to the line containing (4, 6) and (0, 3) 12. Write the equation of a line, in point-slope form, that passes through (3, 7) and (4, -2). ! 13. Write the equation of a line, in point-slope form, that is perpendicular to 𝑦 − 5 = − ! (𝑥 + 2) and passes through the point (2, 7). 14. Translate pre-image ΔJAK where J(5, 1), A(-5, 2), and K(–2, –4) up 4 and to the left 2 units. Graph and list the coordinates of the image. A J J’ ( ______ , ______ ) A’ ( ______ , ______ ) K’ ( ______ , ______ ) K 15. Given pre-image AB where A (3, 4) and B (2, -1), rotate 90 ° clockwise about the origin. Graph and list the coordinates of image A'B' . A A’(_______, _______) B’(_______, _______) B 16. Given ∆ABC with A(0, –2), B(12, 4), and C(16, 0), a. Draw the median AG . b. Write the equation of the line that contains the median AG . __________________________ Standard 3A 1. Write a conditional for the statement, “A rhombus has congruent sides.” 2. “If a shape is a rectangle, then it has 4 right angles.” a. Underline the hypothesis and circle the conclusion. b. Write the converse of the statement. 3. PlaceeachofthefollowingpropertiesintheappropriateregionoftheVenndiagram. Rhombus Parallelogram A. Sidesarecongruent B. Diagonalsbisecteachother C. Oppositesidesarecongruent 4. PlaceeachofthefollowingpropertiesintheappropriateregionoftheVenndiagram. Altitude Median A. Passesthroughavertex B. Bisectstheoppositeside C. Perpendiculartotheoppositeside 5. Jim was given the diagram where BD is a median. His teacher asked him to set up an equation to solve for x. The equation he created is below. Justify why his equation is correct using sound mathematical reasoning. B Jim’s equation: 3x − 10 = 2x + 1 x + 12 4x – 9 A 3x – 10 D 2x + 1 C This equation is correct because: 6. Sheila was given the diagram below and asked to set up an equation to solve for x. The equation she created is below. Justify why her equation is correct using sound mathematical reasoning. Sheila’s equation: x + 32 = 4x − 28 (x + 32)° (4x – 28 )° Sheila’s equation is correct because: 7. Gary was given the following problem and asked to set up an equation to solve for x. The equation he created is below. Justify why his equation is incorrect using sound mathematical reasoning. Problem: Given parallelogram KENT. If KE = 5x − 7, TN = 4x + 2, and NE = 7x + 5 . Find x and KT. Gary’s equation: 4x+2=7x+5. Gary’s equation is correct / incorrect because Standard 3B 1. Given T is between C and L with TC = 2x + 2, TL = 4x − 8, and CL = 5x − 1 , determine whether T bisects CL . Tdoes/doesnotbisect CL because 2. Given two sides of a triangle have lengths of 8 units and 11 units, state a possible length of the the third side, and explain your answer using sound mathmatical resoning. A possible third side length is 3. because Given ΔMOV, MV=3.9, OV=2.7, and MO=1.8, determine the largest angle of the figure. Explain your answer using sound mathematical reasoning. M 3.9 1.8 O 2.7 V The largest angle of the figure is because 4. In ΔRTM, where 𝑚∠R=140 and 𝑅𝑇 ≅ 𝑅𝑀, complete the questions below. a. Classify ΔRTM according to its angles (circle your answers): Obtuse Acute Right b. Classify ΔRTM according to its sides (circle your answers): Scalene 5. ∠1 and ∠5 6. ∠4 and ∠13 7. ∠10 and ∠8 8. ∠10 and ∠12 9. ∠16 and ∠10 10. Given: Isosceles TRANSVERSAL C is the midpoint of BD ∠B and ∠D are right angles Equilateral ANGLE NAME k j 1 2 4 3 5 6 8 7 13 14 16 15 A 9 10 12 11 l m B C D Complete the statement: Δ𝐴𝐵𝐶 ≅ Δ 11. E by Given the diagram, determine if m // l. Justify your answer using relevant mathematical support l is / is not (circle one) parallel to m because: m l 12. Given m∠DBC = ( x + 32 ) ° , m∠DBA = ( 8x − 6 ) ° , and m∠CBA = ( 2x + 27 ) ° , !" ! determine whether BC bisects ∠DBA . D B C A !" ! BC does / does not (circle one) bisect ∠DBA because: _________________________________ _______________________________________________________________________________ B 13. Given ΔABC determine the smallest side of the triangle. Explain your answer using sound mathematical reasoning. 85° 49° C A The smallest side of the triangle is 14. because Given ∆QRS, where m ∠ R = 145 ° and QS=10, RS=8 and SQ=5, complete the questions below. a. Classify ∆QRS according to its angles (circle your answer): Obtuse Acute Right b. Classify ∆ QRS according to its sides (circle your answer): Scalene Isosceles Equilateral 15. Given two sides of a triangle have lengths of 10 cm and 4 cm. Determine which of the following could be a possible third side, circle all that apply. Using relevant mathematical support, explain why you circles the lengths that you did. 3 4 6 9 11 16 The lengths _________________________ could be the third side because 16. Given the diagram, determine if m // l. Justify your answer using relevant mathematical support l is / is not (circle one) parallel to m because: m l