Download LT Chapter 1

Learning Targets Geometry – Chapter #1
Essential
Concept:
4: Expert
3: I get it
2: I kind of get it
Specific Example or Conjecture:
Midpoint
Example #1:
a) Name each midpoint and the segment it bisects.
b) Name all congruent segments. Use the congruence symbol in your
answers.
(1.1)
Midpoint
Example #2:
Find the coordinates of the midpoint of the segment with endpoints (-4, 6)
and (1, 0).
(1.1)
Rays
(1.1)
Example #3:
Are ⃗⃗⃗⃗⃗
𝐴𝐵 and ⃗⃗⃗⃗⃗
𝐵𝐴 the same rays? Explain your reasoning.
1: I am lost
Capture Your Thinking:
Get
it???
Angles
(1.2)
Measure
Example #1: Which angle has the greater measure? Explain your reasoning.
(1.2)
Measure
Example #2:
a) Using a protractor, draw ∠𝐿𝑀𝑁 with a measure of 128°.
b) Now, draw ⃗⃗⃗⃗⃗⃗
𝑀𝑃 so that it is the angle bisector of ∠𝐿𝑀𝑁. Be as
accurate as possible. Add congruency marks to the diagram.
c) Name the congruent angles. Use the congruence symbol and be
careful to name them in a way so there is no confusion.
(1.2)
Angle Addition
(1.2)
Angle Addition
(1.2)
Angle Bisector
Example #3: Find the measure of the unknown angle.
•
⃗⃗⃗⃗⃗ is the angle bisector of ∠𝑅𝑃𝑆. Find the two angle
Example #4: 𝑃𝑇
measures not given in the picture.
Example #5:
What is the ∠𝐴𝐵𝑇 ?
Angle
Vocabulary
(1.3)
Writing Good
Definitions
Polygons
(1.4)
Classifying
Polygons:
(1.4)
Steps for Writing Good Definitions:
Classify the Polygons with the given number of sides:
3
4
5
6
7
8
9
10
11
12
n
Example #1: Which polygon is congruent to ABCDE?
(1.4)
Example #2 Perimeter: Are two polygons with the same perimeter
congruent? If yes, state the reason why, but if no, give a counterexample.
(1.4)
Example #3: In the diagram, ∆𝑻𝑱𝑴 ≅ ∆𝑷𝑯𝑺. Complete each statement.
Triangles
(1.5)
Assumption
•
•
1.
2.
To assume something is true is to _________________________
Things you may assume:
Lines are straight, and if two lines intersect they do so at one point.
All points on a line are collinear and all points in a plane are
coplanar unless planes are shown that they are not coplanar.
• Things you may not assume:
1. Just because two lines look parallel that they are parallel – they
must be marked parallel.
2. Just because two lines look perpendicular that they are
perpendicular – they must be marked perpendicular.
3. Pairs of angles, segments or polygons are not necessarily
congruent unless they are marked appropriately.
(1.5)
(1.5)
Example #1: In the diagrams below, which pairs of lines are
perpendicular? Which pairs of lines are parallel? Which pair of triangles
are congruent?
•
Example #2: Locate a point O so that ∆MOE is an isosceles right
triangle.
Special Quadrilaterals
(1.6):
Venn Diagram:
Problem Solving:
(1.9)
P. 84 - Example #2:
(1.9)
P. 84 - Example #4:
Chapter #1 Learning Objectives:
1.
2.
3.
4.
5.
Learn terminology and notation associated with geometric objects.
Become familiar with objects that have special characteristics.
Begin defining parts of geometric objects.
Translate descriptions into diagrams and vice versa.
Encounter some real-world applications of geometry.
Chapter #1 Construction Objectives:
1. Develop the skills to measure angles and line segments and mark figures appropriately.
2. Review or develop basic construction skills.
Chapter #1 Process Skills:
1.
2.
3.
4.
Develop visual thinking and reading comprehension.
Develop critical thinking and persevere through problem-solving.
Ongoing development of cooperative behavior in small group discussions as well as whole class summaries.
Ongoing development of deductive reasoning in a variety of areas: discussions, homework, assessments.