**Geometry Review**

Chapter: 3

Chapter: 3

SSS Method

(SSS) If three sides of one triangle are congruent to three corresponding sides of another triangle then the triangles are congruent.

Definition of Congruent Triangles:

All pairs of corresponding parts are congruent

In other words means: Triangles which are same

size and shape

**Congruent Triangles**

Congruent Triangles

But after all this is just another tool

that you can put away in your tool box

Congruent Polygons and The Reflexive Property

Postulate #1, The Reflexive Property: Any segment or angle is congruent to itself

Congruent Polygons: All pairs of corresponding parts are congruent

Section 3.1

What are congruent figures?

Section 3.2

Three ways to prove triangles congruent

SAS Method

(SAS) If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

**ASA Method**

(ASA) If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

**CPCTC**

C

ongruent

P

arts of

C

ongruent

T

riangles are

C

ongruent

If two triangles are congruent then the corresponding parts are congruent.

So If ABC = DEF, Then /_ B =/_ E

Using CPCTC in Proofs

Given:BS=UG,BU=SG

Prove:/_SUG=/_BSU

__ ___ ___ ___

Left side of room

Right side of room

Circles

A circle is named by its center:

This circle is named O

CPCTC and Circles

Section 3.3

Review:

A=//r

C=2//r

2

**~**

**~**

Theorem 19:All radii of a circle are congruent

Proofs using circles

**l**

Given:

OR, /_CRB=/_CRA

.

Prove:/_A=/_B

Section 3.4

Beyond CPCTC

Altitudes and Medians

Definition of Median: A line segment drawn from any vertex of the triangle to the midpoint of the opposite side

Definition of Altitude: A line segment drawn from any vertex of the triangle to the opposite side and perpendicular to the side

Note: The line segment may be extended

90

Important Postulate!

Two points determine a line(or ray or segment)

POP QUIZ!

Section 3.5

Overlapping Triangles

Overlapping triangles

Problems using overlapping triangles:

Section 3.6

Types of triangles

Types of triangles

Scalene triangle

- A triangle in which no two sides are congruent

Isosceles triangle

- a triangle in which at least two sides are congruent

equilateral triangle

- A triangle in which all sides are congruent

What triangles are the coolest?

Problems using overlapping triangles:

Types of triangles

Equiangular triangle-

triangle in which all angles are congruent

Acute triangle-

a triangle in which all angles are acute

Right triangle-

a triangle in which one of the angles is a right angle ( the side opposite the right angle is called the hypotenuse. The sides that form the right angles are called the legs.

Obtuse triangle-

is a triangle in which one of the angles is an obtuse angle

Section 3.7

Angle-Side Theorem

Section 3.8

The HL Postulate

All 3 altitudes of a triangle NEVER fall outside the triangle

ASN

a. Two triangles are congruent if 2 sides and an angle of one are congruent to the corresponding parts of the other.

b. If two sides of a right triangle are congruent to the corresponding parts of another right triangle, the triangles are congruent

c. All three altitudes of a triangle fall outside the triangle

d. A median of a triangle does not contain the midpoint of the side to which it is drawn.

If there exists a correspondance between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent.(HL Method)

Can only be used with right triangles

HL Method

1. S

2. A

3. N

4. N

Problems using the HL Method

ANGLE SIDE THEOREMS

If two sides of a triangle are congruent the angles opposite are congruent

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

Continued...

If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side.

if two angles of a triangle are not congruent, then the sides opposite them are not congruent and the longer side is opposite the larger angle

By Oliver and Kirby

A

B

C

D

E

F

What do you call an angle which is adorable?

Acute Angle

Ice-Soceles