Download Chapter Four

Chapter Four
Sophie Havranek and Lily Hartmann
Lesson 4.1 Apply Triangle Sum
Properties
Order by sides:
Equilateral
Order by angles:
Scalene
Isosceles
Acute
Right
Equiangular
Obtuse
Lesson 4.1 Apply Triangle Sum
Properties
Triangle Sum Theorem : The sum of the measures of the interior angles of
a triangle are always equal to 180o
Exterior Angle Theorem: The measure of an exterior angle of a triangle is
equal to the sum of the measure of the two nonadjacent angles.
Lesson 4.2 Apply Congruence and
Triangles
Congruent Figures: All parts of one figure are congruent to
corresponding parts of the other figure. This means corresponding sides
and corresponding angles are congruent.
Congruence Statements:
Two congruence statements could be
Corresponding Angles:
Corresponding Sides:
Lesson 4.2 Apply Congruence and
Triangles
Identify Congruent Parts:
To help you write a congruence statement you can identify all pairs of
corresponding parts.
Use Properties of Congruent Figures:
If you were to know that FG was congruent to QR and FG was 12 and QR
was 2x-4, you could find x.
12=2x-4 16=2x 8=x
Lesson 4.2 Apply Congruence and
Triangles
Prove That Triangles Are Congruent:
know you
triangles are
SSS or SAS or
You have identified all
corresponding parts so
can say that the
congruent by
AAS.
Lesson 4.4 Prove Triangles
Congruent by SSS
Side-Side-Side Congruence Postulate: If three sides of one triangle are
congruent to three sides of of a second triangle then those two triangles
are congruent.
Lesson 4.5 Prove Triangles
Congruent by SAS and HL
Side-Angle-Side(SAS) Postulate: If two sides and the included angle of
one triangle are congruent to two sides and the included angle of a
second triangle, then the two triangles are congruent.
Lesson 4.5 Prove Triangles
Congruent by SAS and HL
Hypotenuse-Leg(HL) Congruence Theorem: If th hypotenuse and a leg of
a right triangle are congruent to the hypotenuse and a leg of a second
right triangle, then the two triangles are congruent.
Lesson 4.6 Prove Triangles
Congruent by ASA and AAS
Angle-Side-Angle(ASA) Congruence Postulate: If two angles and the
included side of one triangle are congruent to two angles and the
included side of a second triangle, then the two triangles are congruent.
Lesson 4.6 Prove Triangles
Congruent by ASA and AAS
Angle-Angle-Side(ASA) Congruence Theorem: If two angles and a nonincluded side of one triangle are congruent to two angles and the
corresponding non-included side of a second triangle, then the two
triangles are congruent.
Lesson 4.6 Prove Triangles
Congruent by ASA and AAS
Flow Proofs:
Lesson 4.7 Use Congruent
Triangles
Lesson 4.7 Use Congruent
Triangles
Lesson 4.7 Use Congruent
Triangles
Lesson 4.8 Use Isosceles and
Equilateral Triangles
Base Angles Theorem: If two sides of a triangle are congruent, then the
angles opposite them are congruent.
Converse of Base Angles Theorem: If two angles of a triangle are
congruent, then the sides opposite them are congruent.
Lesson 4.9 Perform Congruence
Transformations
A transformation is an operation that moves or changes a geometric
figure. The new figure is called an image.
●
●
●
A translation moves every point the same distance and the same
direction.
A rotation turns the figure about a fixed point called the center of
rotation.
A reflection uses a line of reflection to create a mirror image of the
figure.
Lesson 4.9 Perform Congruence
Transformations
A congruence transformation gets translated, reflected, or rotated with
out changing it’s shape or size.
Lesson 4.9 Perform Congruence
Transformations