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FINAL EXAM REVIEW. Chapter 4 Key Concepts. Chapter 4 Vocabulary. congruent figures corresponding parts equiangular Isosceles Δ legs base vertex angle base angles. median altitude perpendicular bisector CONGRUENCE METHODS: SSS SAS ASA AAS HL.

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FINAL EXAM REVIEW

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## FINAL EXAM REVIEW

Chapter 4

Key Concepts

### Chapter 4 Vocabulary

congruent figures

corresponding parts

equiangular

Isosceles Δ

legs

base

vertex angle

base angles

median

altitude

perpendicular bisector

CONGRUENCE METHODS:

SSS

SAS

ASA

AAS

HL

### Defn. of Congruent Triangles

• Two triangles are congruent ( ) if and only if their vertices can be matched up so that the corresponding parts (angles and sides) of the triangles are congruent.

∆ ABC ∆ DEF

ORDER MATTERS!

7

D

A

7

7

E

B

7

A

D

7

F

C

7

AB

DE

BC

EF

B

C

E

F

CA

FD

### SSS Postulate

If three sides of one triangle are congruent to three sides of

another triangle, then the triangles are congruent.

S

B

A

R

C

T

~

ABC = RST by SSS Post.

### SAS Postulate

If two sides and the included angle of one triangle are congruent

to two sides and the included angle of another triangle, then the

triangles are congruent.

F

Q

E

P

G

R

~

EFG = PQR by SAS Post.

### ASA Postulate

If two angles and the included side of one triangle are congruent

to two angles and the included side of another triangle, then the

triangles are congruent.

M

Y

N

Z

L

X

~

XYZ = LMN by ASA Post.

### The AAS (Angle-Angle-Side) Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

B

Y

ABC

XYZ

C

Z

A

X

### The HL (Hypotenuse - Leg) Theorem

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

A

X

ABC

XYZ

Z

B

C

Y

Right triangles

All triangles

SSS Post

SAS Post

ASA Post

AAS Thm

HL Thm

### The Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Iso. Thm.

### Converse to Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Converse to Iso. Thm.

### Corollaries

• An equilateral triangle is also equiangular.

• An equilateral triangle has three 60o angles.

• The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

### Median

• A median of a triangle is a segment from a vertex to the midpoint of the opposite side. Each triangle has three medians.

A

A

.

A

.

.

B

C

B

C

B

C

### Altitude

• The perpendicular segment from a vertex to the line that contains the opposite side.

A

A

A

Acute Triangles

C

C

C

B

B

B

Right Triangles

A

A

A

C

C

C

B

B

B

Obtuse Triangles

C

C

C

B

B

B

A

A

A

Perpendicular Bisector

• A line, ray, or segment that is perpendicular to a segment at its midpoint.

### Theorem

• If a point lies on the perpendicular bisector of a segment, then…

the point is equidistant from the endpoints of the segment.

.

.

.

CONVERSE:

If a point is equidistant from the endpoints of a segment, then… the point lies on the perpendicular bisector of the segment.

### Theorem

• If a point lies on the bisector of an angle then,…

the point is equidistant from the sides of the angle.

.

CONVERSE:

If a point is equidistant from the sides of an angle, then…..the point lies on the bisector of the angle.

### Homework

• Chapter 3-4 Review Olympics W/S

• pg. 164 #1-9 (multiple choice)