Download Lesson 4.1 - Advanced Geometry: 2(A)

Lesson 4.1 & 4.2 ADV:
1. Triangle Sum Theorem
2. Properties of Isosceles Triangles
4.1 Warm Up:
• Have a pen and a pencil out for this opening activity.
• On your own, write everything you know about triangles
in pencil.
• You will have 3 minutes to write this information in your
notes.
• Then you will have discussion time with the person next
to you to add anything new in pen.
• Make a decision about who in your group will investigate
an acute triangle and who will investigate an obtuse
triangle.
Investigation #1:
• Split a piece of paper with your desk-mate.
• One of you will draw (using a straightedge) an acute
angle on your half and the other person will draw an
obtuse angle on his/her half.
• Cut out your triangle.
• Tear off the three angles and arrange them on a line.
(Draw a line if this helps.)
• What do you notice about the angle measures?
Triangle Sum Conjecture:
• The sum of the measures of the angles in a
triangle is __________.
Proof of the Triangle Sum
Conjecture:
• Why do angles 2, 4, and 5 add up to 180º? Use
deductive reasoning to explain.
4.1 Example #1:
Classifying Triangles by Sides:
• Name the triangle that fits the given description:
Isosceles Triangles:
(4.2) Investigations 1 & 2:
• In your notes, do the Investigations on p.
207 – 208.
• After each investigation, summarize each
conjecture in your notes.
Isosceles Triangles:
A
• Conjectures:
Isosceles Triangle Conjecture: If a triangle is
Isosceles, then _____________________________.
If AB  AC , then
C
Converse of the Isosceles Triangle Conjecture: If a triangle has
two congruent angles, then __________________________.
If B  C , then
B
(4.2) Practice #1:
• Solve for x and y.
(4.2) Example #2:
• Solve for the variables.
(4.2) Example #3:
Homework:
• P. 203-205: 5, 6, 9, 10, 16
• P. 208-209: 8, 9, 18, 19, 25
Closing Activity:
• Write any new conjectures in your LT. Add
any helpful example of each conjecture.
Be sure to define any new words.