Chapter 4 Congruent Triangles

__Section
4.1 Classifying Triangles__

**Triangle**a three sided
polygon

__Triangle Sum Theorem__:
The sum of
the measures of the interior angles of a triangle is 180 degrees.

**Acute Triangle**3 acute angles

**Right Triangle**1 right angle

**Obtuse Triangle**1 obtuse angle

**Equiangular Triangle**3 congruent angles

**Equilateral Triangle**3 congruent sides

**Isosceles Triangle**at least 2 congruent sides

**Scalene Triangle**no congruent sides

__Section 4.2
Angles of Triangles__

**Triangle Sum Theorem:
The sum of
the measures of the interior angles of a triangle is 180 degrees. **What are the measures of
the angles of an equilateral triangle?

** Third Angle
Theorem:** If **
two angles of one** triangle are congruent to **
two angles of a** **second** triangle, then the **third**
**
angles** of the triangles are **congruent**.

** Exterior Angle
Theorem:**
The measure of an ** exterior angle** of a triangle is equal to the
** sum** of the
measures of the ** two remote interior angles**.

**Corollary 4.1: **The acute angles
of a right triangle are complementary.

**Corollary 4.2: **There can be at most one right or obtuse angle in a triangle.

__Section
4.3 Congruent Triangles__

**Congruent Triangles:** Triangles
that are the same size and shape.

Triangles have six measurable parts (3 angles and 3 sides)

If all six __corresponding__ parts are congruent
in the two triangles, then the triangles are congruent.

**Definition of
Congruent Triangles:**

Two Triangles are congruent IFF their corresponding parts are congruent

** CPCTC**:

Theorem 4.4: Congruence of triangles is Reflexive, Symmetric, and Transitive.

__Section
4.4 Proving Congruence: SSS, SAS__

**Postulate 4.1:** ** (Side-Side-Side
Congruence)**: If the sides of one triangle are congruent to
the

**Postulate 4.2:** ** (Side-Angle-Side
Congruence)**: If two sides and the

__Section 4.5 Proving Congruence:
ASA, AAS__

**Postulate 4.3:** ** (Angle-Side-Angle
Congruence)**: If two angles and the

**Postulate 4.4:** ** (Angle-Angle-Side
Congruence)**: If two angles and a

**Legs**: the two sides that form the right angle

**Hypotenuse**: the side opposite the right angle.

__Right Triangle Congruence:__

**Theorem 4.6****:**
** (Leg-Leg
Congruence)**: same as______

**Theorem 4.7:**
** (Hypotenuse-Angle
Congruence)**: same as____

**Theorem 4.8:**
** (Leg-Angle
Congruence)**: same as_____

**Postulate 4.4:** ** (Hypotenuse-Leg
Congruence)**: same as____

__Section
4.6
Isosceles Triangles__

**Legs**: the two congruent sides

**Base**: the non-congruent side

**Vertex Angle**: the angle formed by the legs.

**Base Angles**: the angle formed by the base and
one leg.

**Isosceles
Triangle Theorem**: If two sides of a triangles are
congruent, then the angles opposite those sides are congruent.

**This is also know as the Base Angles
Theorem**

**Converse of
Isosceles Triangle Theorem: **If two angles of a
triangle are congruent, then the sides opposite those angles are congruent.

**This is also know as the Converse of
the Base Angles Theorem**

**Corollary 4.3:** A triangle is
equilateral if and only if it is equiangular.

**Corollary 4.4: ** Each angle of an
equilateral triangle measures 60 degrees.

EXAMPLE: