1. Entry Task – page 40

2. Lesson 1-6 Part I Constructing Congruent Segments & Angles
Basic Constructions
Lesson 1-6 Part I
Constructing Congruent Segments & Angles

3. Learning Targets I will be able to:
Use a compass and straightedge to construct congruent segments and angles;
Use a compass and straightedge to construct specific figures without using a ruler or protractor.

4. Sketch, Draw, & Construct
Sketch – a freehand rough drawing; not drawn to scale; should look like what is described and be labeled appropriately
Draw – an accurate representation of the described figure using a ruler and/or protractor; should still be labeled appropriately
Construct – an accurate representation of the described figure but without using any measuring devices (rulers or protractors); should still be labeled appropriately

5. 3 Types of Constructions
Compass & Straightedge
Patty Paper
Computer software
Geometer’s Sketchpad
Geogebra

6. Constructing Congruent Segments
Draw a segment, 𝑋𝑌 , like the one below.
Construct 𝐶𝐷 so that it is congruent to 𝑋𝑌 using only a compass and straightedge. Be sure to label the new segment. X Y

7. Construct a line segment 𝐴𝐵 such that 𝐴𝐵=3 𝑃𝑄−𝑅𝑆P Q R S

8. Constructing Congruent Angles
Construct ∠𝐶 so that it is congruent to ∠𝐵. B

9. Now try an obtuse angle…
Construct ∠M so that it is congruent to ∠𝐿. L

10. Construct an angle, ∠𝑃𝐷𝐵 , such that 𝑚∠𝑃𝐷𝐵=𝑚∠𝑇+𝑚∠𝐾K T

11. Homework
Practice Worksheet 1-6

12. Entry Task

13. Lesson 1-6 Part II Constructing Bisectors of Segments & Angles
Basic Constructions
Lesson 1-6 Part II
Constructing Bisectors of Segments & Angles

14. Learning Targets for Day 2
I will be able to:
Use patty paper to construct segment and angle bisectors;
Use a compass and straightedge to construct segment and angle bisectors;
Use a compass and straightedge to construct specific figures without using a ruler or protractor.

15. Finding the right bisector…
In this investigation, you will discover how to find the perpendicular bisector of a segment.
Step 1: Draw a segment on a piece of patty paper. Label it 𝑃𝑄 .

16. Step 2: Fold your patty paper so that endpoints P and Q land exactly on top of each other. In other words, they coincide. Crease your paper along the fold.

17. Step 3: Unfold your paper. Draw a line in the crease
Step 3: Unfold your paper. Draw a line in the crease. What is the relationship of this line to 𝑃𝑄 ? Use your ruler and protractor to verify your observations.
In the students notes, there are a few other steps for students to investigate. Drawing points on the perpendicular bisector and comparing the distances between the point and each endpoint of the segment. They should find that the distances are the same. The can use a ruler to compare or even a compass, but the compass will tear the patty paper if the students aren’t careful. This idea is the basis for how we will construct a perpendicular bisector with a compass and straightedge.

18. Perpendicular Bisector Conjecture
If a point is on the perpendicular bisector of a segment, the it is
________________________ from each of the endpoints of the segment.
I added this slide to show that every point on line CD (which is the perpendicular bisector of segment AB) is the same distance from each endpoint. Students will likely see it as forming an isosceles triangle but may not remember the name.
the same distance
*The reverse of this conjecture is also true and we will use that to construct a perpendicular bisector with a compass and straightedge.

19. Bisecting a segment with a compass & straightedge
We will use the compass to find points that are the same distance from each endpoint of a given segment.
Draw a segment on your paper. Label the endpoints A and B.
Demonstrate on the doc camera or on the board how to construct bisectors using a compass & straightedge A B

20. What if I can’t make arcs on each side of the segment?
Make two sets of arcs on the same side of the segment by changing the compass setting.

21. Bisecting Angles
Step 1: On a piece of patty paper, draw a large-scale angle and label it ∠𝑃𝑄𝑅.

22. Step 2: Fold your paper so that 𝑄𝑃 and 𝑄𝑅 coincide (overlap perfectly)
Step 2: Fold your paper so that 𝑄𝑃 and 𝑄𝑅 coincide (overlap perfectly). Crease the paper along the fold.

23. Step 3: Unfold your paper and draw a ray with endpoint Q along the crease. Does the ray bisect ∠𝑃𝑄𝑅? How can you tell?

24. Bisecting Angles with a compass and straightedge…
Find a point on each side of the angle that is the same distance from the vertex of the angle. Draw an arc to represent this. Label these points A and B.
Draw an arc from point A that is in the interior of the angle.
Using the same compass setting as step b, draw an arc from point B that is in the interior of the angle so that it intersects with the arc you drew from point A.
The point where these two arcs intersect is a point on the angle bisector. Use your straightedge to connect this point to the vertex.

25. Try another one…

26. Assignment Page 46 (13-21 all, 26, 31)
You will have some class time to work on this during the next class
Read Lesson 1-7 on pages about Midpoint and Distance in the Coordinate Plane.
Take notes on what you think are the key ideas for the lesson.
We will do examples in class next time.
Since so many students may not have a compass at home, I may decided to have students read the next lesson as their homework (Lesson 1-7 about Midpoints and Distance) and then give them class time to work on the constructions during the first half of the next class. It will be the only block class of the week. I will then go over the PowerPoint lesson for 1-7 during the 2nd half of the block class and still be mostly on schedule to do lesson 1-8 on Thursday and start reviewing on Friday.