with your partner, answer questions 1-4 on page 575. (questions on next slide.) use whatever tools...
TRANSCRIPT
With your partner, answer questions 1-4 on page 575. (Questions on next slide.)
Use whatever tools seem best (available on front table).
Keep track of your answers, as well as how you solved each problem, including what tools you used and how you used them.
Warm-Up: February 26, 2015
Pag
e 5
75
#1
-4
Homework Questions?
ConstructingInvestigation 7B
Advanced Integrated Math I
Warm-Up Answers
Page 575 #1
Page 575 #2
Page 575 #3-4
Work with your partner to answer page 575 #5-6
Warm-Up: February 27, 2015
Homework Questions?
Warm-Up Answers
Page 576 #7-10
Assignment
See textbook for #10
Page 576
You have the following tools available:◦ Ruler◦ Compass◦ Protractor
You want to construct the following shapes:◦ Circle◦ Square◦ Line◦ 45° angle
Which tool(s) can you use to construct each one? Provide all possible answers.
Warm-Up: March 2, 2015
Homework Questions
Compasses, Angles, and Circles
Section 7.06Advanced Integrated Math I
Drawings are often rough sketches. They are aids to problem solving.
A construction is a guaranteed recipe.◦ A construction shows how to accurately draw a
figure with a specified set of tools.◦ Constructions are solutions to problems.
Drawing vs. Constructing
Compass – Any device that allows you to move a pencil a fixed distance around a point.
Straightedge – Any object with a straight edge that allows you to draw a line segment.◦ A true straightedge does not have markings to
measure distance. Measuring Devices – Rulers and protractors Paper – Not just a surface. Can be folded to
use symmetric properties. Can be cut and rearranged.
String and tacks – Can be used to construct circles, ellipses, spirals, and other curves.
Construction Tools
Minds in Action
Think-Pair-Share
1) Do you see Tony’s triangle? Explain how you know his triangle has the correct side lengths.
2) The title of this lesson is “Compasses, Angles, and Circles,” but this lesson has not yet mentioned compasses, angles, or circles. How do Sasha’s and Tony’s ruler tricks both imitate a compass?
3) How can a compass make a geometric construction easier?
1. Draw a line segment.2. Without measuring, construct its midpoint.
You-Try
You-Try Solution
A midpoint is the point on a segment that is halfway between the two endpoints.
Equidistant means “the same distance.” The perpendicular bisector of a segment
is the line that is perpendicular to the segment at the segment’s midpoint.
Vocabulary
Each point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.
Perpendicular Bisector Theorem
Use converse of the Perpendicular Bisector Theorem
Finding Midpoint – Method 2
An altitude is a perpendicular segment from a vertex of a triangle to the line that contains the opposite side.◦ Every triangle has three altitudes.
More Vocabulary
A median is a segment that connects the vertex of a triangle to the midpoint of the opposite side.◦ Every triangle has three medians.
A midline is a segment that connects the midpoints of two sides of a triangle.◦ Every triangle has three midlines.
More Vocabulary
Do each of the following constructions, and write down how you did it.
You may not use rules, protractors, or other measuring tools.
1) Draw a line. Then construct a line perpendicular to the first line.
2) Draw a line. Then construct a line parallel to the first line.
3) Draw an angle. Then construct its bisector.
You-Try’s (with partner)
Read Section 7.06 (pages 577-581) Page 582 #10-16 Page 584 #1-8 (Investigation 7B Reflection)
Assignments
Page 582
Do each of the following constructions with your partner, and write down how you did it.
You may not use rulers, protractors, or other measuring tools.
1) Draw a line. Then construct a line perpendicular to the first line.
2) Draw a line. Then construct a line parallel to the first line.
3) Draw an angle. Then construct its bisector.
Warm-Up: March 3, 2015
1) Draw a line. Then construct a line perpendicular to the first line.
2) Draw a line. Then construct a line parallel to the first line.
3) Draw an angle. Then construct its bisector.
An altitude is a perpendicular segment from a vertex of a triangle to the line that contains the opposite side.◦ Every triangle has three altitudes.
More Vocabulary
A median is a segment that connects the vertex of a triangle to the midpoint of the opposite side.◦ Every triangle has three medians.
A midline is a segment that connects the midpoints of two sides of a triangle.◦ Every triangle has three midlines.
More Vocabulary
Homework Questions?
Netbooks Needs to be installed
Geogebra
Read Section 7.06 (pages 577-581) Page 582 #10-16 Page 584 #1-8 (Investigation 7B Reflection)
Assignments
Page 584