Grade 6 / angles: the basics 56 exercises corrected

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ChingQuizz : 6 exercises available for Quizz assessment : 1. Names and notations of angles E.9998 Consider the rhombus ABCD shown below : An angle has been coded. Which of the following notations represent this angle? a ∠ ABI b ∠ IAB c ∠ CAB d ∠ BAD E.9997 Below we consider the rectangle ABCD : Name the three angles coded in the figure. E.1670 Consider the configuration below where three angles have been coded : 1 Name the coded angle with vertex D in four different ways. 2 Name the vertex-coded angle I in four different ways. 3 In how many ways can the coded vertex angle C be named? Hint: we don’t ask to give all its names. 2. Nature of the angles E.1656 Definition: we categorize angles into 5 groups : Consider the plane provided with the two straight lines and points shown below : Give the nature of each of the angles below : a ABC b DEG c DEF d FEG e JHI f HJI g JIH E.6582 Consider the figure below : 1 Name the five angles labeled in this figure and state their types. 2 What are the types of angles MDB and CIB ? https://chingmath.fr quizzChap/1002 chapExoCorrec/9998 sacados/9998 IABCD chapExoCorrec/9997 sacados/9997 IABCD chapExoCorrec/1670 sacados/1670 ABCDIMNP chapExoCorrec/1656 sacados/1656 AnglenulAngleaiguAngledroitAngleobtusAngleplat ABCDEFGIJH chapExoCorrec/6582 sacados/6582 ABCDIMN
E.1660 In each case, draw an angle of the nature indicated and give the measure of your angle: a Un angle nul b Un acute angle c Un right angle d Un angle obtu e An angle plat E.2425 Consider the figure below : Give the name and nature of all the angles coded on the figure above. E.2968 In the plane, consider the figure be-low where the quadrilateral ABCD ; the point I belongs to the segment [ CD ] and J is a point of [ AB ] . 1 Give the name of each of the angles coded on the figure. 2 Using the segments drawn in this figure, name, in this figure, all the angles : a aigus b obtus c plats d nuls E.3008 In the plane, consider the quadrilat-eral ABCD and M a point on the diagonal [ DM ] . 1 Name the set of acute angles in this figure. 2 Name all the obtuse angles in this figure. 3 Name, if they exist: a the (s) angle (s) null (s) . b the (s) angle (s) flat (s) . 3. Comparison of angles without measurements E.5585 Consider the quadrilateral ABCD shown below : 1 Without justification, compare the measurements of the angles ∠ ADC and ∠ ABC . 2 Using a square, compare the measures of the angles ∠ DAB and ∠ DCB . E.656 We define the angle shown here and the hexagon that defines six exterior angles. The six angles, highlighted in the poly-gon below, are labeled using the six let-ters of the alphabet shown below : ¸ ˛ ‚ ‹ " ” Alpha Beta Gamma Delta Epsilon Éta 1 Construct a protractor for the angle shown at the begin-ning of the exercise. 2 Using the template, compare each angle of the hexagon with the angle on the template. https://chingmath.fr chapExoCorrec/1660 sacados/1660 chapExoCorrec/2425 sacados/2425 ABCDEF chapExoCorrec/2968 sacados/2968 ABCDIJ chapExoCorrec/3008 sacados/3008 ABCDM chapExoCorrec/5585 sacados/5585 ABCD chapExoCorrec/656 sacados/656 ¸˛‚‹"”
4. Angle measurement with protractor representation E.10634 Consider the configuration below, where points O , B , and A are aligned : 1 Give the nature of the following angles : AOB ; AOC ; BOD ; AOE ; BOF 2 Give the measure, in degrees, of the following angles : a AOC = : : : : : : : : : o b BOD = : : : : : : : : : o c AOE = : : : : : : : : : o d BOF = : : : : : : : : : o E.10635 Consider the configuration below where points O , B , A are aligned : Give the measure, in degrees, of the following angles : a AOC = : : : : : : : : : o b BOC = : : : : : : : : : o c AOD = : : : : : : : : : o d BOD = : : : : : : : : : o E.10636 Consider the configuration below where points O , B , A are aligned : Give the measure, in degrees, of the angle COD . E.2548 Consider the simplified ˇ protractor ı below of center O . It has been divided into 4 equal parts ˇ A ı, ˇ B ı, ˇ C ı, ˇ D ı. 1 Give the measure in degrees of the angle ∠ xOz . Justify the measure of this angle. 2 Consider the half line [ Or ) such that ∠ yOr = 120 o . Which division of the protractor intercepts the half line [ Or ) ? 3 Knowing that the angle ∠ yOs is an obtuse angle, what divisions of the protractor can be intercepted by the line [ Os ) . 4 Give a frame for the measure of the angle ∠ tOy when the line [ Ot ) intercepts the division ˇ B ı. E.2547 Consider the simplified ˇ protractor ı below. It has been split into 9 equal parts ; note that the central part has been redivided into two equal parts. 1 Determine the measure of the angle xOz . 2 Consider the following angles : yO‘ = 106 o ; xOm = 12 o ; xOn = 84 o xOp = 92 o ; yOq = 53 o ; xOr = 59 o yOs = 150 o ; xOt = 174 o ; yOu = 29 o xOw = 113 o Each division of the protractor is intercepted by only one of the preceding angles. Complete the following table : 5. Angle measurement https://chingmath.fr chapExoCorrec/10634 sacados/10634 OABCDEF chapExoCorrec/10635 sacados/10635 OABCD chapExoCorrec/10636 sacados/10636 OABCD chapExoCorrec/2548 sacados/2548 xzyOABCD chapExoCorrec/2547 sacados/2547 xzyOABCDGHIJEF DivisionAngleinter-ceptantladivisionABCDEFGHIJ
E.11004 Download the file below and open it with Geogebra: https://chingmath.fr/plus-11004-mesure.ggb Using the protractor, determine the measurements of the four angles of the quadrilateral: a ABC = : : : b BCD = : : : c CDA = : : : d DAB = : : : E.2424 Using the protractor, take the nec-essary measurements to complete the table below : Angle yAx FBE tCu wDG Measurement (in degrees) E.1671 Using the protractor, take the nec-essary measurements to complete the table below : yAx ; FBE ; tCu ; wDG Angle yAx FBE tCu wDG Measurement (in degrees) E.1664 1 Name then measure, with the help of the reporter, each of the angles coded on the figure below : 2 Give the measurement of the following two angles : ∠ TV W et ∠ TWV E.11092 Consider the triangle XY Z shown below : Name, then give the measure of each of the angles of this triangle. E.3923 Name the three angles coded on the figure below, then give the measure of these three angles : https://chingmath.fr chapExoCorrec/11004 sacados/11004 fichierPlus/11004/ https://chingmath.fr/plus -11004-measure.ggb chapExoCorrec/2424 sacados/2424 yAxBFEtCuDwG chapExoCorrec/1671 sacados/1671 yAxBFEtCuDwG chapExoCorrec/1664 sacados/1664 BACFHGMLKTVW chapExoCorrec/11092 sacados/11092 XYZ chapExoCorrec/3923 sacados/3923 ABCM
E.2549 Give the names of the coded angles in the figure below and their measurements : E.1661 The figure below shows the quadri-lateral ABCD and the point E belonging to the segment [ BC ] . Using the protractor, complete the table below with the four coded on the figure and their measurements : Angle Mesure E.6583 Consider the figure below : Determine the measure of the following angles : a ∠ FDE b ∠ DFG c ∠ DBE d ∠ BAE E.1673 The figure below shows a quadrilat-eral ABCD . M is a point of segment [ AD ] : 1 Name, then measure, to with the reporter, the four an-gles of quadrilateral ABCD . 2 Give the measure of the ∠ BMC angle. E.10374 Consider the rectangle ABCD shown below and the points E , F , G belonging to the sides of this triangle: Arrange in ascending order the measure of the angles : ∠ FDE , ∠ DEF , ∠ EFG et ∠ FGC . https://chingmath.fr chapExoCorrec/2549 sacados/2549 ABCDO chapExoCorrec/1661 sacados/1661 ABCDE chapExoCorrec/6583 sacados/6583 ABCDEFGHIJ chapExoCorrec/1673 sacados/1673 ABCDM chapExoCorrec/10374 sacados/10374 EFGABCD
6. Drawing of angles E.2421 Consider the figure below composed of segment [ AB ] and 14 points : 1 Among the seven points C 1 , C 2 , . . . , C 7 , determine the unique point C verifying the measure : BAC =30 o . 2 Among the seven points D 1 , D 2 , . . . , D 7 , determine the unique point D verifying the measure : ABD =35 o . E.1672 We provide the plane with the two segments [ AB ] and [ DE ] , as well as the half-line [ EG ) : 1 Place a point C in the plane so as to have : ABC = 25 o 2 a Using the protractor, measure the angle DEG . b Place the single point, denoted F , on the half-line [ EG ) making the measurement : EDF =40 o . E.2437 Consider the figure below composed of the segment [ AB ] and the half-line [ Ax ) . 1 Determine the measure of the angle ∠ xAB . 2 Place on the half line [ Ax ) the point C checking the fol-lowing measure : ∠ CBA = 25 o 3 Give the measure of the angle ∠ ACB . E.2980 Using your drawing instruments, re-produce the figure below : 7. Drawing Triangles (2 Angles, 1 Side): Introduction E.2422 Consider the segment [ AB ] below : https://chingmath.fr chapExoCorrec/2421 sacados/2421 C1C2C3C4C5C6C7D1D2D3D4D5D6D7AB chapExoCorrec/1672 sacados/1672 ABDEG chapExoCorrec/2437 sacados/2437 ABx chapExoCorrec/2980 sacados/2980 110o145o42o5cm6cmABCDE chapExoCorrec/2422 sacados/2422 AB
Among the points below, determine the single point C verify-ing the following two relations : BAC = 45 o ; ABC = 35 o Determine the location of this point. E.6584 Consider the figure below : Among the points M 1 to M 9 , which point should be chosen on the figure for a construct a triangle ABC verifying the following measures : ∠ BAC = 50 o ; ∠ ABC = 18 o ; ∠ ACB = 112 o 8. Triangles tracing E.1662 The figure opposite was created freehand. Using geometry instruments, re-produce this figure. E.10004 The figure opposite was created freehand. Using geometry instruments, re-produce this figure. E.10637 The figure opposite was created freehand. Using geometry instruments, re-produce this figure. E.10002 Draw the triangle DEF having measure : DE = 8 cm ; ∠ EDF = 35 o ; ∠ FED = 50 o E.2551 In the frame above, draw the following triangles : 1 triangle ABM verifying: MAB = 85 o ; ABM = 35 o 2 triangle ANC verifying: NAC = 30 o ; NCA = 130 o 3 triangle BPC verifying: PBC = 39 o ; PCB = 116 o https://chingmath.fr chapExoCorrec/6584 sacados/6584 ABM1M2M3M4M5M6M7M8M9 chapExoCorrec/1662 sacados/1662 7cmABC70o45o chapExoCorrec/10004 sacados/10004 5cm55oDEF chapExoCorrec/10637 sacados/10637 7cmABC70o45o chapExoCorrec/10002 sacados/10002 chapExoCorrec/2551 sacados/2551 ABC
E.3911 The ABC triangle has been drawn out of frame. In order to redraw it from the segment [ A B ] , transfer the angles ∠ BAC and ∠ ABC to A and B respec-tively. 9. Drawing triangles (1 angle, 2 sides) E.10003 The figure opposite was created freehand. Using geometry instruments, re-produce this figure. E.2666 Draw the triangle ABC having mea-sure : CAB = 115 o ; BC = 8 cm ; AB = 5 cm E.2423 1 Freehand draw any ABC triangle. Then transfer the following indications to it: AB = 8 cm ; AC = 6 cm ; CAB = 45 o 2 Using your measuring instruments, construct the triangle ABC respecting the indications above. E.1667 The figure opposite was created freehand. Using geometry instruments, re-produce this figure. 10. Drawing triangles E.10411 The two figures below were made freehand : Using geometric instruments, reproduce these figures E.10001 1 Draw the segment [ DE ] of length 6 cm . 2 Draw the circle C with center E and radius 5.5 cm . 3 Draw the half line [ Dx ) denoting the following angle mea-sure : ∠ xDE = 58 o 4 Justify that there are two possibilities for placing a point F that allows one to draw the triangle DEF with the following measures : DE = 6 cm ; EF = 5.5 cm ; ∠ FDE = 58 o E.11810 L’exercice n’existe pas. 11. Drawing of polygons E.2603 Reproduce the figure below to full size : https://chingmath.fr chapExoCorrec/3911 sacados/3911 ABAB chapExoCorrec/10003 sacados/10003 6cm7cm55oDEF chapExoCorrec/2666 sacados/2666 chapExoCorrec/2423 sacados/2423 chapExoCorrec/1667 sacados/1667 ABC6cm7cm70o chapExoCorrec/10411 sacados/10411 7cmABC65o50o5cm55oDEF chapExoCorrec/10001 sacados/10001 sacados/11810 chapExoCorrec/2603 sacados/2603
E.2969 Reproduce the figure below, observ-ing the indications shown : E.2552 The figure below is not full-scale. It represents a pentagon ABCDE . 1 Make this figure full-scale. 2 Determine the measure ¸ o of the angle DCB using the protractor. E.3009 The figure below is made up of two triangles. Reproduce this figure, respecting the dimensions indicated : E.6388 Reproduce the figure below : 12. Tracing polygons (difficulty with right-angled triangle) E.6320 Reproduce the following figure using a ruler and a compass : https://chingmath.fr ABCDE105o122o7cm4cm chapExoCorrec/2969 sacados/2969 6cm5;5cm7cm6cmABCDEF140o127o60o213o chapExoCorrec/2552 sacados/2552 25o105o¸oABCDE5;3cm4cm6cm11cm chapExoCorrec/3009 sacados/3009 38o8cm6cmABC72o42oD chapExoCorrec/6388 sacados/6388 ABC40o9;5cm7cmD35o60oE154o108o chapExoCorrec/6320 sacados/6320 ABC7cm5cmD9;5cmE6cm
E.2886 In the plane, consider the figure below : 1 Give the nature of each of the following triangles ABC , ECB , ABD , ACF . 2 Reproduce this figure in true sizes on your copy. E.6345 Reproduce the following figure using a ruler and a compass : 13. Tracing of particular triangles and angles E.5582 We consider the two triangles repre-sented below : 1 a What is the nature of the triangle ABC ? b What is the measure of the angle ∠ ABC ? 2 a What is the nature of the triangle DEF ? b What is the measure of the angle ∠ EDF ? E.5605 Reproduce the figure below : E.6636 Consider the figure below : Reproduce this figure in full size. 14. Write a construction program https://chingmath.fr chapExoCorrec/2886 sacados/2886 ABC6cm4cm5cm7cmDFE chapExoCorrec/6345 sacados/6345 ABC9cm8cmD6cm7;5cmEF5cm chapExoCorrec/5582 sacados/5582 ABCDEF70o chapExoCorrec/5605 sacados/5605 ABCDE6cm7cm chapExoCorrec/6636 sacados/6636 5cm50o6cm65o42o4cm5cmABCDEFG
E.3924 Give the plot program for the figure below : https://chingmath.fr chapExoCorrec/3924 sacados/3924 42o72ox80oy100oABCMNP7;5cm3cm