Presentation is loading. Please wait.

Presentation is loading. Please wait.

Basic Geometric Constructions-Part 1 C. N Colón Geometry St. Barnabas High School.

Published byTodd Potter Modified over 8 years ago

Similar presentations

Presentation on theme: "Basic Geometric Constructions-Part 1 C. N Colón Geometry St. Barnabas High School."— Presentation transcript:

1

2 Basic Geometric Constructions-Part 1 C. N Colón Geometry St. Barnabas High School

3 Objectives Students will –Copy a segment –Copy an angle –Bisect a segment –Bisect an angle –Construct a Perpendicular Bisector of a line segment directly and from a point near a line as well as on a line.

4 How to Copy a Segment A B 1)Since a segment is a part of a line, we’ll start by drawing a ray that is somewhat longer than our intended segment, and call the starting point A’. A’ 2)Place the Needle end of the compass on point A, and adjust its length to match the distance AB. 3)Without changing the width of the compass, put the Needle end of the compass on point A’, and draw the arc to cross your ray. Label the point of intersection B’. You’ve just copied AB to A’B’ B’

5 Copy An Angle A B 1)Since an angle is two rays with a common vertex we’ll start by drawing a ray and call ray B’A’. A’ 2)Place the Needle end of the compass on point B, and make an arc that crosses over from BA to BC. 3)Without changing the width of the compass, put the Needle end of the compass on point B’, and draw the arc crossing B’A’ long enough to more than cross where B’C’ will be. B’ C 4)Now go back to the original angle, and put your needle on the point of intersection of AB and the arc. Measure the distance along the arc to the ray BC. 5) Without changing the width of the compass, put your needle on the point of intersection of the arc and B’A’. Make an arc that crosses the first arc you drew on this new angle. 6) Draw a ray from B’ thru the point of intersection of the two arcs. Label a point on the ray as C’. You’ve copied the angle ABC as A’B’C’. C’

6 Bisecting a Segment A B 1)Place the needle of your compass on A. Make its width more than half-way to B, and make a half-circle. 2) Without changing the width of the compass, put the needle of your compass on B. Make a half-circle that overlaps the first one. 3) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the segment AB, and is perpendicular to AB.

7 Bisecting an Angle A B 1)Place the needle of your compass on B. Draw an arc that crosses both BA and BC. 3) Place the needle of the compass on D, and set the width to match more than half the distance to E. Make a half-circle. 5) Draw a line that connects the two points of intersection of the two half-circles. That new line is both a bisector of the angle ABC. C D E 2) Label the intersection of the arc and BA “D”, and the intersection of the arc and BC “E”. 4) Leave the compass width as it is. Place the needle of the compass on E, and make a half- circle overlapping the previous half-circle.

8 Perpendicular line Construction Aim: Divide a line in half at 90º Perpendicular Bisector Perpendicular Line from a point NEAR a line P P P Perpendicular Line from a point ON a line

9 Perpendicular Bisector A Step1 Aim: Divide a line in half at 90º Click to start Rule a line (leaving some space on each side of the line) Home

10 Perpendicular Bisector A Compass point Set your compass to about ¾ of the line length Step1 Aim: Divide a line in half at 90º Home

11 Perpendicular Bisector Compass point Set your compass to about ¾ of the line length Step1 Aim: Divide a line in half at 90º Home

12 Perpendicular Bisector Compass point Set your compass to about ¾ of the line length Step1 Aim: Divide a line in half at 90º Home

13 Perpendicular Bisector Compass point Arc into space each side of the line Step1 Aim: Divide a line in half at 90º Home

14 Perpendicular Bisector Compass point Arc into space each side of the line Step1 Aim: Divide a line in half at 90º Home

15 Perpendicular Bisector Compass point Arc into space each side of the line Step1 Aim: Divide a line in half at 90º Home

16 Perpendicular Bisector Compass point Arc into space each side of the line Step1 Aim: Divide a line in half at 90º Home

17 Perpendicular Bisector Compass point Arc into space each side of the line Step1 Aim: Divide a line in half at 90º Home

18 Perpendicular Bisector B Compass point Arc into space each side of the line Step1Step2 Aim: Divide a line in half at 90º Keep the compass the same Home

19 Perpendicular Bisector Compass point Arc into space each side of the line Step1Step2 Aim: Divide a line in half at 90º Keep the compass the same Home

20 Perpendicular Bisector Compass point Arc into space each side of the line Step1Step2 Aim: Divide a line in half at 90º Keep the compass the same Home

21 Perpendicular Bisector Compass point Arc into space each side of the line Step1Step2 Aim: Divide a line in half at 90º Home

22 Aim: Divide a line in half at 90º Perpendicular Bisector C With this point Use a ruler to join this point Step1Step2Step3Home

23 Perpendicular Bisector Aim: Divide a line in half at 90º And half way This should be 90º 90º 1212 1212 Perpendicular bisector Step1Step2Step3 The EndCircumcircle Home

24 Circumcircle Do the Perpendicular Bisectors of the sides of a triangle meet at one point? This? Step1Step2Step3The EndCircumcircleHome

25 Circumcircle Do the Perpendicular Bisectors of the sides of a triangle meet at one point? OR This? Step1Step2Step3The EndCircumcircleHome

26 Circumcircle Do the Perpendicular Bisectors of the sides of a triangle meet at one point? Step1Step2Step3The EndCircumcircleHome

27 Perpendicular Line from a Point A Aim: Construct a line at 90º through a point near a line P Step1 Rule a line Mark a point near the line (about 4cm away is fine) Leave some space on either side of the line Click to start Home

28 Perpendicular Line from a Point A Compass point Set your compass to reach over the line so the arc will cut twice Aim: Construct a line at 90º through a point near a line P Step1Home

29 Perpendicular Line from a Point Compass point Set your compass to reach over the line so the arc will cut twice Aim: Construct a line at 90º through a point near a line P Step1Home

30 Perpendicular Line from a Point Compass point Aim: Construct a line at 90º through a point near a line P Move your compass to one side Step1Home

31 Perpendicular Line from a Point Compass point Aim: Construct a line at 90º through a point near a line P Step1Home

32 Perpendicular Line from a Point Compass point Aim: Construct a line at 90º through a point near a line P Step1Home

33 Perpendicular Line from a Point Compass point Aim: Construct a line at 90º through a point near a line P Step1Home

34 Perpendicular Line from a Point B Aim: Construct a line at 90º through a point near a line P Step1Step2Home

35 P Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Keep the compass the same Step1Step2Home

36 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point near a line Keep the compass the same Step1Step2Home

37 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point near a line Keep the compass the same Step1Step2Home

38 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point near a line Step1Step2Home

39 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point near a line Step1Step2Home

40 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point near a line Step1Step2Home

41 P Perpendicular Line from a Point C Compass point Arc into space each side of the line Keep the compass the same Aim: Construct a line at 90º through a point near a line Step1Step2Step3Home

42 P Perpendicular Line from a Point Compass point Arc into space each side of the line Keep the compass the same Aim: Construct a line at 90º through a point near a line Step1Step2Step3Home

43 P Perpendicular Line from a Point Compass point Arc into space each side of the line Keep the compass the same Aim: Construct a line at 90º through a point near a line Step1Step2Step3Home

44 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point near a line Step1Step2Step3Home

45 P Perpendicular Line from a Point D With this point Use a ruler to join this point Aim: Construct a line at 90º through a point near a line Step1Step2Step3Home

46 P Perpendicular Line from a Point This should be 90º 90º Perpendicular Line Step1Step2Step3 The End Aim: Construct a line at 90º through a point near a line Home

47 Perpendicular Line from a Point A Aim: Construct a line at 90º through a point on a line P Step1 Click to start Rule a line Mark a point on the line (not in the middle) Leave some space on either side of the line Home

48 Perpendicular Line from a Point A Compass point Aim: Construct a line at 90º through a point on a line P Mark an arc on both sides of point P Step1Home

49 Perpendicular Line from a Point A Compass point Aim: Construct a line at 90º through a point on a line P Mark an arc on both sides of point P Step1Home

50 Perpendicular Line from a Point A Compass point Aim: Construct a line at 90º through a point on a line P Mark an arc on both sides of point P Step1Home

51 Perpendicular Line from a Point A Compass point Aim: Construct a line at 90º through a point on a line P Mark an arc on both sides of point P Step1Home

52 Perpendicular Line from a Point A Compass point Aim: Construct a line at 90º through a point on a line P Mark an arc on both sides of point P Step1Home

53 Perpendicular Line from a Point A Compass point Aim: Construct a line at 90º through a point on a line P Mark an arc on both sides of point P Step1Home

54 Perpendicular Line from a Point Compass point Set compass to ¾ the length of the arc Aim: Construct a line at 90º through a point on a line P Step1Step2Home

55 Perpendicular Line from a Point Compass point Set compass to ¾ the length of the arc Aim: Construct a line at 90º through a point on a line P Step1Step2Home

56 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Home

57 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Home

58 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Home

59 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Home

60 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Home

61 P Perpendicular Line from a Point C Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Step3Home

62 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Step3Home

63 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Keep the compass the same Step1Step2Step3Home

64 P Perpendicular Line from a Point Compass point Arc into space each side of the line Aim: Construct a line at 90º through a point on a line Step1Step2Step3Home

65 P Perpendicular Line from a Point D With this point Use a ruler to join this point Aim: Construct a line at 90º through a point on a line Step1Step2Step3Home

66 P P Perpendicular Line from a Point This should be 90º 90º Perpendicular Line Step1Step2Step3 The End Aim: Construct a line at 90º through a point on a line Home

Download ppt "Basic Geometric Constructions-Part 1 C. N Colón Geometry St. Barnabas High School."

Similar presentations

Copying and Constructing Triangles Math 2 - Lesson 59 Mr. Lopez.

Copying and Constructing Triangles Math 2 - Lesson 59 Mr. Lopez.
District maths coordinator

District maths coordinator
Constructing Lines, Segments, and Angles

Constructing Lines, Segments, and Angles
Construction in Geometry

Construction in Geometry
DO NOW Sketch each figure. CD GH AB Line m Acute ABC XY II ST.

DO NOW Sketch each figure. CD GH AB Line m Acute ABC XY II ST.
Geometric Constructions: Congruent Segments and Congruent Angles Geometry Mr. Zampetti Unit 2, Day 1.

Geometric Constructions: Congruent Segments and Congruent Angles Geometry Mr. Zampetti Unit 2, Day 1.
Perpendicular line Construction Aim: Divide a line in half at 90º Perpendicular Bisector Perpendicular Line from a point NEAR a line P P P Perpendicular.

Perpendicular line Construction Aim: Divide a line in half at 90º Perpendicular Bisector Perpendicular Line from a point NEAR a line P P P Perpendicular.
constructions Bisecting an Angle constructions  Centre B and any radius draw an arc of a circle to cut BA and BC at X and Y.  Centre X any radius draw.

constructions Bisecting an Angle constructions  Centre B and any radius draw an arc of a circle to cut BA and BC at X and Y.  Centre X any radius draw.
Section 1-5: Constructions SPI 32A: Identify properties of plane figures TPI 42A: Construct bisectors of angles and line segments Objective: Use a compass.

Section 1-5: Constructions SPI 32A: Identify properties of plane figures TPI 42A: Construct bisectors of angles and line segments Objective: Use a compass.
Bisecting Segments and Angles

Bisecting Segments and Angles
Basic Geometric Constructions By: Mr. Erlin Geometry 1 Tamalpais High School.

Basic Geometric Constructions By: Mr. Erlin Geometry 1 Tamalpais High School.
Ruler &Compass Constructions

Ruler &Compass Constructions
Perpendicular Bisector of a Segment and Angle Bisector

Perpendicular Bisector of a Segment and Angle Bisector
J.Byrne 20141. Geometry involves the study of angles, points, lines, surfaces & solids An angle is formed by the intersection of two straight lines. This.

J.Byrne Geometry involves the study of angles, points, lines, surfaces & solids An angle is formed by the intersection of two straight lines. This.
3.1 Duplicating Segments and Angles

3.1 Duplicating Segments and Angles
1.6 Basic Constructions.

1.6 Basic Constructions.
Step-by-Step Constructions Perpendicular Through A Point (off a line) Equilateral Triangle What’s Wrong with SSA? Circumcenter Incenter Centroid Perpendicular.

Step-by-Step Constructions Perpendicular Through A Point (off a line) Equilateral Triangle What’s Wrong with SSA? Circumcenter Incenter Centroid Perpendicular.
Creating Constructions Unit 7. Word Splash Constructions Construction – creating shapes using a straight edge and a compass Straight edge – clear,

Creating Constructions Unit 7. Word Splash Constructions Construction – creating shapes using a straight edge and a compass Straight edge – clear,
Constructing Bisectors. Bisecting a Segment A B 1)Place the needle of your compass on A. Make its width more than half-way to B, and make a half-circle.

Constructing Bisectors. Bisecting a Segment A B 1)Place the needle of your compass on A. Make its width more than half-way to B, and make a half-circle.
CHAPTER 1: Tools of Geometry

CHAPTER 1: Tools of Geometry

Similar presentations

Ads by Google