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Chapter 4 Congruent Triangles

Chapter 4 Vocabulary Scalene Triangle

Isosceles Triangle

Equilateral Triangle

Acute Triangle

Right Triangle

Obtuse Triangle

Equiangular Triangle

Interior Angles

Exterior Angles

Congruent Figures

Corresponding Parts

Leg

Hypotenuse

Legs

Vertex Angle

Base

Base Angles

Postulates and Theorems Theorem 4.1 – Triangle Sum Theorem

Theorem 4.2 – Exterior Angle Theorem

Postulate 19 – Side Side Side (SSS) Congruence Postulate

Postulate 20 – Side Angle Side (SAS) Congruence Postulate

Theorem 4.5 – Hypotenuse Leg (HL) Congruence Theorem

Postulate 21 – Angle Side Angle (ASA) Congruence Postulate

Theorem 4.6 – Angle Angle Side (AAS) Congruence Theorem

Theorem 4.7 – Base Angles Theorem

Theorem 4.8 – Converse of Base Angles Theorem

4.0 Triangles and Venn Diagrams Types of Triangles…

Classified by Sides…

Classified by Angles…

Venn Diagrams

1.) Band and Choir

2.) Math Team, Science Olympiad and LINK

4.1 Apply Triangle Sum Properties

Theorem 4.1 – Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°

Theorem 4.2 – Exterior Angles Theorem The measure of an exterior angle is equal to the sum of the

measures of the two nonadjacent interior angles.

Linear Pair Postulate

Vertical Angles Theorem

Find the measures of the indicated angles given the provided information.

1.) m∢2 = 85° and m∢3 = 40°

m∢4 = and m∢1 =

2.) m∢1 = 30° and m∢2 = 3·m∢3 + 10°

m∢2 = and m∢3 =

4.2 Apply Congruence and Triangles

4.3 Proving Triangles Congruent by SSS

Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a

second triangle, then the two triangles are congruent.

Use the graph to determine if ΔABC ≅ ΔDEF.

4.4 Proving Triangles Congruent by SAS

Side-Angle-Side (SAS) Congruence 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.

State the postulate the can be used to prove the triangles congruent

1.

2. 3.

4.

Statement Reason

Given: Prove:

4.5 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.

Angle-Angle-Side (AAS) Congruence Theorem If two angles and a non-included 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.

State the postulate the can be used to prove the triangles congruent

1.

2.

3.

4.

5.

6.

4.6 Use Congruent Triangles

Corresponding Parts of Congruent Triangles are Congruent (CPCTC):

Given: Prove:

Statement Reason

4.7 Isosceles and Right Triangles

Isosceles Triangle

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.

Solve for x and y. 1.

2.

Right Triangle

Hypotenuse Leg (HL) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to

the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

State the postulate the can be used to prove the triangles congruent

1.

2.

3.

4.

5.

6.