### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

# Chapter 3: Congruent Triangles

No description
by

## Oliver Tidswell

on 14 January 2014

Report abuse

#### Transcript of Chapter 3: Congruent Triangles

Geometry Review
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
Full transcript