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Guided Notes for Chapter 4
Lesson 4.1 Triangle Sum Conjecture
Triangle Sum Conjecture
The sum of the measures of the angles in every triangle is
.
Third Angle Conjecture
If two angles of one triangle are equal in measure to two angles of
another triangle, then the third angle is each triangle is equal in measure
to the
in the other triangle.
Lesson 4.2 Properties of Special Triangles
In an isosceles triangle, the angle between the two congruent sides is
called the
angle, and the other two angles are called the base
angles. The side between the two base angles is called the
of the
isosceles triangle. The other two sides are called the
.
Isosceles Triangle Conjecture
If a triangle is isosceles, then its
angles are
Converse of the Isosceles Triangle Conjecture
If a triangle has two
angles, then it is an
.
triangle.
Lesson 4.3 Triangle Inequalities
Triangle Inequality Conjecture
The
of the lengths of any two sides of a triangle is
the length of the third side.
than
Side-Angle Inequality Conjecture
In a triangle, if one side is longer than another side, then the angle
opposite the longer side is
than the angle opposite the
side.
If you extend one side of a triangle beyond its vertex, then you have
constructed an
at that vertex.
Each exterior angle of a triangle has an
angle and a pair
of
angles. The
angles are the two
angles in the triangle that do not share a vertex with the exterior angle.
Triangle Exterior Angle Conjecture
The measure of an
angle of a triangle is
the measures of the
angles.
the
of
Lesson 4.4 Are There Congruence Shortcuts?
There are
different ways that the same three parts of two triangles
may be congruent.
An angle that is included between two sides of a triangle is called an
. A side that is included between two angles of a
triangle is called an
.
SSS Congruence Conjecture
If the three sides of one triangle are congruent to the three side of
another triangle, then the
.
SAS Congruent Conjecture
If two sides and the included angle of one triangle are congruent to two
sides and the
angle of another triangle, the triangles are
.
Lesson 4.5 Are There Other Congruence Shortcuts?
ASA Congruence Conjecture
If two angles and the
side of one triangle are congruent to two
angles and the
side of another triangle, then the triangles are
.
SAA Congruence Conjecture
If two angles and a
side of one triangle are congruent to
the
angles and side of another triangle, then the triangles
are
.
Lesson 4.6 Corresponding Parts of Congruent Triangles
The definition of congruent triangles states that if two triangles are
congruent, then the
parts of those congruent triangles are
congruent. This is referred to as
.
Lesson 4.7 Flowchart Thinking
A
is a concept map that shows all the steps in a complicated
procedure in proper order. Arrows connect the boxes to show how facts
lead to conclusions.
To present your reasoning in flowchart form, create a
Place each statement in a box. Write the logical reason for each
statement beneath its box.
Lesson 4.8 Proving Isosceles Triangle Conjecture
Vertex Angle Bisector Conjecture
In an isosceles triangle, the bisector of the vertex angle is also the
and the
to the
.
Equilateral/Equiangular Triangle Conjecture
Every
triangle is
and, conversely, every
triangle is equilateral.
.