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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

FINAL EXAM REVIEW

Chapter 4

Key Concepts


Chapter 4 vocabulary
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
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
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
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
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
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
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


Summary of ways to prove triangles congruent
Summary of Ways to Prove Triangles Congruent

Right triangles

All triangles

SSS Post

SAS Post

ASA Post

AAS Thm

HL Thm


The isosceles triangle theorem
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
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
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
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
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
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.


Theorem1
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
Homework

  • Chapter 3-4 Review Olympics W/S

  • pg. 164 #1-9 (multiple choice)


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