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Chapter 4:
Discovering and
Proving Triangle
Properties
- 4.1 Triangle Sum
Conjecture
- The sum of the
measures of the angles
in every triangle is 180
degrees.
- The sum of the
measures of the angles
in every triangle is 180
degrees.
- 4.2 Properties of Isosceles
triangles
- Vertex angle: The angle between
the two congruent sides The
base angles are the other two
angles. The side between the two
base angle is called the base.
The other two sides are caused
legs.
- Vertex angle: The angle between
the two congruent sides The
base angles are the other two
angles. The side between the two
base angle is called the base.
The other two sides are caused
legs.
- 4.3 Triangle
Inequality
conjecture
- The sum of the lengths
of any two sides of a
triangle is more than the
length of the third side.
- The sum of the lengths
of any two sides of a
triangle is more than the
length of the third side.
- 4.4 and 4.5 Are there
congruent shortcuts?
- SSS
- SAS
- ASA
- SAA
- SSA
- AAA
- Three pairs of
congruent angles
- Works
- Works
- Three pairs of
congruent angles
- Two pair of
congruent sides
and one pair of
congruent angles.
- Doesn't work
- Doesn't work
- AAA
- Two pair of congruent
angles and one pair of
congruent sides(nots
not between the pair of
angles)
- Works
- Works
- SSA
- Two pair pair of
congruent angle and one
pair of congruent
sides(sides between the
pair of angles)
- Works
- Works
- SAA
- Two pairs of congruent sides
and one pair of congruent
angles.(angles between the pair
of sides.
- Works
- Works
- ASA
- Three pairs of
congruent sides
- Works
- Works
- SAS
- 4.6 Corresponding Parts
of Congruent triangles
- If you use a congruence
shortcut, then you can
use CPCTC to show that
any of their
corresponding parts are
congruent
- 4.7
Flowchart
thinking
- Flowchart proofs
are when you fill
in boxes for a
proof instead of
a two column
proof.
- 4.8 Proving
Special
Triangle
Conjectures
- Vertex
angleBisector
Conjecture
- In an isosceles
triangle the
bisector of the
vertex angle is
also equiangular
and equilateral.
- In an isosceles
triangle the
bisector of the
vertex angle is
also equiangular
and equilateral.
- Vertex
angleBisector
Conjecture
- Flowchart proofs
are when you fill
in boxes for a
proof instead of
a two column
proof.
- If you use a congruence
shortcut, then you can
use CPCTC to show that
any of their
corresponding parts are
congruent
- SSS
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