2.  TEKS Focus:  (5)(B) Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge.  (1)(E) Create and use representations to organize, record, and communicate mathematical ideas.  (1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.

3.  A compass is a geometric tool used to draw circles and parts of circles called arcs.  A construction is a geometric figure drawn using a straightedge and a compass.  A straightedge is a ruler with no markings on it.

4.  A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint.  Perpendicular lines are two lines that intersect to form right angles. Symbol for perpendicular is .

5.  Refer to Pearson pages 27-30 for step by step instructions for these constructions: ◦ Constructing congruent segments ◦ Constructing congruent angles ◦ Constructing a segment bisector (that is not perpendicular) ◦ Constructing the perpendicular bisector ◦ Constructing the angle bisector  Also use the following website: http://www.mathopenref.com/tocs/con structionstoc.html

6.  Only two constructions are shown after this slide, both for angles.

7. Construct an angle congruent to ∡A. Step 1: Use a straight edge to draw a ray with endpoint D. A D

8. Construct an angle congruent to ∡A. Step 2: Place the compass point at A and draw an arc that intersects both sides of ∡ A. Label the intersections points B and C. D A B C

9. Step 3: Using the same compass setting, place the compass point at D and draw an arc that intersects the ray. Label the intersection E. D E Construct an angle congruent to ∡A. A B C

10. Step 4: Place the compass point at B and open it to the distance BC. Tighten the compass to keep its distance. A B C Construct an angle congruent to ∡A. D E

11. Step 5: Place the point of the compass at E, without changing its size, and draw an arc. Label its intersection with the first arc F. A B C D E Construct an angle congruent to ∡A. F

12. A B C Step 6: Use a straight edge to draw DF D E F Construct an angle congruent to ∡A.

13. Construct the bisector of ∡A. Step 1: Place the point of the compass at A and draw an arc. Label its points of intersection with ∡A as B and C. A B C A

14. Step 2: Without changing the compass setting, draw intersecting arcs from B and C. Label the intersection of the arcs as D. Construct the bisector of ∡A. A B C D

15. Step 3: Use a straight edge to draw AD. AD bisects ∡A. A B C D Construct the bisector of ∡A.