1. 10/31/20151.4: Geometry using Paper Folding 1.4: Geometry Using Paper Folding Expectations: G1.1.3: Perform and justify constructions, including midpoint of a line segment and bisector of an angle, using straightedge and compass. G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems.

2. 10/31/20151.4: Geometry using Paper Folding Constructions Diagrams created according to certain rules, using only a few specified geometric tools.

3. 10/31/20151.4: Geometry using Paper Folding Perpendicular Lines Defn: Two coplanar lines are perpendicular ( ⊥ ) iff they intersect to form a ____________. l m l ⊥ m

4. 10/31/20151.4: Geometry using Paper Folding Parallel Lines Defn: Two ____________ lines are parallel iff they do not intersect. m n m || n

5. 10/31/20151.4: Geometry using Paper Folding Two Perpendiculars Theorem 1. Fold the paper and crease it. Draw a line down the crease and label it. 1. Fold the paper and crease it. Draw a line down the crease and label it l. 2. Fold l onto itself and crease the paper. Label this line. 2. Fold l onto itself and crease the paper. Label this line m. 3. What relationship exists between l and m ?

6. 10/31/20151.4: Geometry using Paper Folding Two Perpendiculars Theorem 4. Mark a point on line l other than the point where l and m intersect. Call this point P. Fold you paper through P such that l lies on itself. Draw line n through this crease.

7. 10/31/20151.4: Geometry using Paper Folding Two Perpendiculars Theorem 5. What relationship exists between l and n ? 6. What relationship exists between m and n ? Your answers to 5 and 6 are called conjectures (statements you think are true based on observations).

8. 10/31/20151.4: Geometry using Paper Folding Two Perpendiculars Theorem If 2 coplanar lines are each perpendicular to the same line, then the lines are ___________ to each other.

9. 10/31/20151.4: Geometry using Paper Folding Challenge Given a line and a point not on the line, determine a paper folding procedure that will allow us to determine the shortest distance between the line and the point.

10. 10/31/20151.4: Geometry using Paper Folding Some new terms

11. 10/31/20151.4: Geometry using Paper Folding Segment Bisector Defn: A line, ray or segment is a segment bisector iff it splits the original segment into 2 ____________________________. A B l l bisects AB

12. 10/31/20151.4: Geometry using Paper Folding Midpoint of a Segment Defn: Point M is the midpoint of AB iff M is _____________ A and B and AM ____MB. _____________ A and B and AM ____MB. A M B M is the midpoint of AB.

13. 10/31/20151.4: Geometry using Paper Folding Perpendicular Bisector Defn: A bisector of a segment is a __________________________ of the segment iff it is perpendicular to the segment. m AB m is the perp bis of AB.

14. 10/31/20151.4: Geometry using Paper Folding Angle Bisector Defn: A line (BD) or a ray (BD) is an angle bisector iff D is in the interior of the angle and it splits the given angle into ____________________________. A CD B BD bisects ∠ B

15. 10/31/20151.4: Geometry using Paper Folding Perpendicular Bisector Theorem 1. Fold your paper. Label the crease line l. Label 2 points on l, A and B. 2. Fold A onto B. Call this line m. 3. Label the intersection of l and m point P.

16. 10/31/20151.4: Geometry using Paper Folding Perpendicular Bisector Theorem 4. What appears to be true about l and m ? 5. What is true about AP and BP? 6. Using your results from 4 and 5, how is m related to AB?

17. 10/31/20151.4: Geometry using Paper Folding Perpendicular Bisector Theorem 7. Identify 4 other points on m. Label these points Q, R, S, T. 8. Determine AQ and BQ; AR and BR; AS and BS; and AT and BT.

18. 10/31/20151.4: Geometry using Paper Folding Perpendicular Bisector Theorem 9. What is true about the distance between any point on the perpendicular bisector of a segment and the endpoints of the segment?

19. 10/31/20151.4: Geometry using Paper Folding Perpendicular Bisector Theorem If a point lies on the perpendicular bisector of a segment, then it is

20. 10/31/20151.4: Geometry using Paper Folding Angle Bisector Theorem 1. Fold two intersecting lines, l and m. Label the point of intersection P and one point on each line such that the lines form ∠ APB. 2. Fold l onto m.

21. 10/31/20151.4: Geometry using Paper Folding Angle Bisector Theorem 3. Draw line q through the crease. 4. What relationship exists between q and ∠ APB? 5. Locate 3 points on q and label them C, D, and E.

22. 10/31/20151.4: Geometry using Paper Folding Angle Bisector Theorem 6. Calculate the distances from C, D, and E to l and m. 7. Make a conjecture about the relationship between points on an angle bisector and the sides of the angle.

23. 10/31/20151.4: Geometry using Paper Folding Angle Bisector Theorem If a point lies on the bisector of an angle, then it is

24. Which statement is true about the figure shown below? A.AB ⊥ CD B.AC || CD C.AD ⊥ AB D.AB ⊥ AC E.AC = CD 10/31/20151.4: Geometry using Paper Folding

25. The notation FG represents: A.the length of a line. B.the length of a segment. C.the length of a ray. D.two points. E.a plane. 10/31/20151.4: Geometry using Paper Folding

26. 10/31/20151.4: Geometry using Paper Folding

27. 10/31/20151.4: Geometry using Paper Folding No assignment for section 1.4