copying an angle
DESCRIPTION
Copying an Angle. Zac Coblentz 5 th hour Mr. Novak Honors geometry. Step 1. Start with angle BAC that we will copy. Step 2. Make a point P that will be the vertex of the new angle. Step 3. From P, draw a ray PQ. This will become one side of the new angle. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/1.jpg)
Zac Coblentz
5th hour
Mr. Novak
Honors geometry
Copying an Angle
![Page 2: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/2.jpg)
Step 1
Start with angle BAC that we will copy.
![Page 3: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/3.jpg)
Step 2
Make a point P that will be the vertex of the new angle.
![Page 4: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/4.jpg)
Step 3
From P, draw a ray PQ. This will become one side of the new angle.
•This ray can go off in any direction.
•It does not have to be parallel to anything else.
•It does not have to be the same length as AC or AB.
![Page 5: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/5.jpg)
Step 4
Place the compass on point A, set to any convenient width.
![Page 6: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/6.jpg)
Step 5
Draw an arc across both sides of the angle, creating the points J and K as shown.
![Page 7: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/7.jpg)
Step 6
Without changing the compass width, place the compass point on P and draw a similar arc there, creating point M as shown.
![Page 8: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/8.jpg)
Step 7
Set the compass on K and adjust its width to point J.
![Page 9: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/9.jpg)
Step 8
Without changing the compass width, move the compass to M and draw an arc across the first one, creating point L where they cross.
![Page 10: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/10.jpg)
Step 9
Draw a ray PR from P through L and onwards a little further. The exact length is not important.
![Page 11: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/11.jpg)
Done. The angle ∠RPQ is congruent (equal in measure) to angle ∠BAC.
![Page 12: Copying an Angle](https://reader036.vdocument.in/reader036/viewer/2022080916/56812ee7550346895d948398/html5/thumbnails/12.jpg)
Proof
1. Line segments AK, PM are congruent
2. Line segments AJ, PL are congruent
3. Line segments JK, LM are congruent
4. Triangles ∆AJK and ∆PLM are congruent
5. Angles BAC, RPQ are congruent.
Both drawn with the same compass width.
Three sides congruent (triangle SSS postulate)
CPCTC postulate. Corresponding parts of congruent triangles are congruent