Download Lesson 4.2 File

Lesson 4.2: Properties of Isosceles Triangles
In this lesson you will:
 discover how the angles of an isosceles triangle are related
 make a conjecture about triangles that have two congruent angles
Recall from Chapter 1 that an isosceles triangle is a triangle
with at least two ______________ sides.
In this lesson you’ll discover some properties of isosceles
triangles.
Investigation 4.2.1: “Base Angles in an Isosceles Triangle”
A.) Below are two angles. Both are labeled C . These angles will be the vertex angles of
two isosceles triangles. Place a point A on one ray of each angle.
C
C
B.) Copy the segment CA onto the other side of the angle to make segment CB. Connect
points A and B.
C.) You have constructed two isosceles triangles. Explain how you know they are isosceles.
D.) Name the base ________ and the base angles _________________.
E.) Use your protractor to compare the measures of the base angles. What relationship do
you notice?
F.) State your observation as your next conjecture, and then add it to your conjecture list.
Isosceles Triangle Conjecture (C-18)
If a triangle is isosceles, then its base angles _________________________________________.
Equilateral triangles have at least two congruent sides, so they fit the
definition of isosceles triangles. That means any properties you discover
for isosceles triangles will also apply to equilateral triangles. How does
the Isosceles Triangle Conjecture apply to equilateral triangles?
You can switch the “if” and “then” parts of the Isosceles Triangle Conjecture to obtain
the converse of the conjecture. Is the converse of the Isosceles Triangle Conjecture
true? Let’s investigate.
Investigation 4.2.2: “Is the Converse True?”
Suppose a triangle has two congruent angles. Must the triangle
be isosceles?
A.) Draw a segment and label it AB . Draw an acute angle
at point A. This angle will be a base angle. See step 1 above as an example. (Why can’t
you draw an obtuse angle as a base angle?)
B.) Copy A at point B on the same side of AB . Label the intersection of the
two rays point C. (See step 2 above as an example.)
C.) Use your compass to compare the lengths of sides AC and BC . What
relationship do you notice? What does this mean you can conclude about the
triangle?
D.) State your observation as your next conjecture, and add to your conj. list.
Converse of the Isosceles Triangle Conjecture (C-19)
If a triangle has two congruent angles, then it is ______________________________________.
ASSIGNMENT: ______________________________________________________