Angle Bisectors – Worksheet A The worksheet is provided in a variety of sizes/formats.

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1 Angle Bisectors 1 2 3 4 5 1 2 3 4 5 Only using a compass and ruler…. 1) Create a line starting at A, perpendicular to BC. (To start, you need to mark two places that are equidistant from A. Then, you can construct a perpendicular bisector.) The line has been angled at A. 2) Repeat the same process to make a perpendicular bisector but join it to A. (Start by finding two places equidistant from A on both lines.) B C B A C A Is the perpendicular bisector actually perpendicular now? 3) Follow the same process. Which number does your bisector hit? 4) Angle BAC is 100° Can you make an angle of 50° without using a protractor? Which number does the line bisector hit? 1 2 3 4 5 B 1 2 3 4 B 5 A C 100° C A What can we say about this line and BAC?

Perpendicular Bisector 90° Cut in half.

Angle Bisector B A C

2 1 Answers 1 Angle Bisectors 1 2 3 4 5 1 2 3 4 5 Only using a compass and ruler…. 1 1) Create a line starting at A, perpendicular to BC. (To start, you need to mark two places that are equidistant from A. Then, you can construct a perpendicular bisector.) The line has been angled at A. 2) Repeat the same process to make a perpendicular bisector but join it to A. (Start by finding two places equidistant from A on both lines.) B C C B A Answers A Is the perpendicular bisector actually perpendicular now? 3) Follow the same process. Which number does your bisector hit? 2 4) Angle BAC is 100° Can you make an angle of 50° without using a protractor? Which number does the line bisector hit? 1 1 2 3 4 5 B 1 2 3 4 B 5 A C 100° C A What can we say about this line and BAC?

2 3 1 2 Answers 2 Angle Bisectors 1 2 3 1 4 2 3 2 1 3 1 3 2 4 Only using a compass and ruler…. 2 2 3 1) Bisect the angle BAC. Which number does it hit? 2) Bisect the angle BAC. Which number does it hit? B 1 2 B 3 1 4 2 3 A A C C 3) Create a 45 ° angle at A. Which number does it hit? (How can we make a 90° angle first?) 4) Which number is equidistant from all sides of this triangle? First, construct a line that is equidistant from AB and AC. 1 2 1 3 B 2 1 3 2 4 B C Answers A A C

1 Angle Bisectors 1 2 3 4 5 1 2 3 4 5 Only using a compass and ruler…. 1) Create a line starting at A, perpendicular to BC. (To start, you need to mark two places that are equidistant from A. Then, you can construct a perpendicular bisector.) The line has been angled at A. 2) Repeat the same process to make a perpendicular bisector but join it to A. (Start by finding two places equidistant from A on both lines.) B C B A C A Is the perpendicular bisector actually perpendicular now? 3) Follow the same process. Which number does your bisector hit? 4) Angle BAC is 100° Can you make an angle of 50° without using a protractor? Which number does the line bisector hit? 1 2 3 4 5 B 1 2 3 4 B 5 A C 100° C A What can we say about this line and BAC?

Angle Bisectors Only using a compass and ruler…. 2 1) Bisect the angle BAC. Which number does it hit? 2) Bisect the angle BAC. Which number does it hit? B 1 2 B 3 1 4 2 3 A A C C 3) Create a 45 ° angle at A. Which number does it hit? (How can we make a 90° angle first?) 4) Which number is equidistant from all sides of this triangle? First, construct a line that is equidistant from AB and AC. 2 1 3 B 1 3 2 4 B C A A C

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