2. 3.4 Constructing Angle Bisectors Objectives: I CAN discover methods of constructing an angle bisector. I CAN explore how to construct special angles by dividing and combining 60o and 90o angles. 1 Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

3. Sketch, Draw, Construct When you ___________ an equilateral triangle, you should use you geometry tools for accuracy. You may use a protractor to measure angles and a ruler to measure the sides. When you ___________ an equilateral triangle, you freehand a triangle that looks like an equilateral triangle. No geometry tools needed. When you ___________ an equilateral triangle with a compass and straightedge, you don’t rely on measurements from a protractor or a ruler. This guarantees that you triangle is equilateral. draw sketch construct Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

4. P. 158 Investigation Draw an angle. Find a method for constructing the bisector of the angle.

5. Investigations 1 & 2: p.157-158 Constructing Angle Bisector C8 Angle Bisector Conjecture If a point is on the bisector of an angle, then it is ______________ from the sides of the angle. equidistant Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

6. Bisecting an Angle Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

7. 6 1.Draw a large angle on your paper and label it PQR. 2.With the point of the compass on Q, stretch out the compass as far as you like and make an arc across the entire angle. 3.Put the point of the compass on the first intersection and make an arc inside the angle. 4.Without changing the compass, put the point on the other intersection and make another arc inside the angle. You should now have an X. 5.Connect the vertex and the X with a ray. Mark the congruencies. Serra - Discovering Geometry Chapter 3: Using Tools of Geometry Construction 6: Angle Bisector P Q R 1 2 3 4 http://www.mathopenref.com/constbisectangle.html

8. Match each geometric construction with its diagram. Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

9. Construct a figure with the given specifications Serra - Discovering Geometry Chapter 3: Using Tools of Geometry