1. 6.6/6.7 Isosceles Triangles, Altitudes and Medians
Learning Objective: To apply the Isosceles triangle theorem and its converse, write proofs using isosceles triangles, and to identify and explore the properties of medians and altitudes.
Warm-up (IN)
Complete with < or >.
1. AB___BC
2. BC___AC
Solve each equation. B
<
65º
< A
60º
55º C
15 Minutes - The first part of the warm-up will be a review of the last lesson, and the 2nd is an algebra review to prepare the students for the algebra that will be done in the notes and homework with isosceles triangles.
20 minutes – Check answers to even problems from HW, then to over any questions. 15 2
4/3

2. Notes Isosceles Triangle Theorem -
Learning Objective: To apply the Isosceles triangle theorem and its converse, write proofs using isosceles triangles, and to identify and explore the properties of medians and altitudes.
Notes
Isosceles Triangle Theorem -
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. T A D
Vertex angle
legs
Converse -
41 minutes for notes
Essential Questions:
What is the isosceles triangle theorem and it’s converse?
If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent.
base
Base angles

3. EX 1 – B Paragraph proof!! A C D E
Learning Objective: To apply the Isosceles triangle theorem and its converse, write proofs using isosceles triangles, and to identify and explore the properties of medians and altitudes.
EX 1 – A B D C E 1 2
Paragraph proof!!
Essential Questions:
How can you use the Isosceles triangle theorem to write a paragraph proof?

4. Segment from a vertex to the midpoint of the opposite side
Learning Objective: To apply the Isosceles triangle theorem and its converse, write proofs using isosceles triangles, and to identify and explore the properties of medians and altitudes.
Median of a Triangle -
Segment from a vertex to the midpoint of the opposite side
Altitude of a Triangle -
A perpendicular segment from a vertex to the line that contains the opposite side.
Essential Questions:
What are the median and altitude of a triangle?

5. Learning Objective: To apply the Isosceles triangle theorem and its converse, write proofs using isosceles triangles, and to identify and explore the properties of medians and altitudes.
*In an isosceles triangle, the median, altitude and angle bisector (from the vertex angle) are all the same segment.
Essential Questions:
How are the median, altitude and angle bisector related in an isosceles triangle?

6. Learning Objective: To apply the Isosceles triangle theorem and its converse, write proofs using isosceles triangles, and to identify and explore the properties of medians and altitudes.
EX 2 – A B D C E 5 X
Essential Questions:
How can I use this information, and the isosceles triangle theorems to find missing values in triangles.

7. 8 minutes for CKC
The students will do the Checking Key Concepts on separate paper to trade and grade.

8. Out – Compare and contrast the altitude and the median of a triangle.
Summary – Today, I understand…
Or I’m not too sure about…
5 minutes for Summary and closing questions.
I will have the students do the Out as a ticket out.
HW – p. 317#9-15 odd, 20, p. 322 #1,2,6,7,11,12