Upload
tholene-wongyu
View
52
Download
1
Tags:
Embed Size (px)
Citation preview
Proving Triangles Congruent
Free powerpoints at http://www.worldofteaching.com
Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.
Corresponding PartsCorresponding Parts
∆ABC ≅ ∆ DEF
B
A C
ED
F
1. AB ≅ DE2. BC ≅ EF3. AC ≅ DF4. ∠ A ≅ ∠ D5. ∠ B ≅ ∠ E6. ∠ C ≅ ∠ F
Side-Angle-Side (SAS)Side-Angle-Side (SAS)
1. AB ≅ DE2. ∠A ≅ ∠ D3. AC ≅ DF
∆ABC ≅ ∆ DEF
B
A
C
E
D
F
included angle
Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)
1. ∠A ≅ ∠ D2. AB ≅ DE3. ∠ B ≅ ∠ E
∆ABC ≅ ∆ DEF
B
A
C
E
D
F
included
side
Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)
1. ∠A ≅ ∠ D2. ∠ B ≅ ∠ E3. BC ≅ EF
∆ABC ≅ ∆ DEF
B
A
C
E
D
F
Non-included side
Warning:Warning: No SSA Postulate No SSA Postulate
A C
B
D
E
F
NOT CONGRUENT
There is no such thing as an SSA
postulate!
Warning:Warning: No AAA Postulate No AAA Postulate
A C
B
D
E
F
There is no such thing as an AAA
postulate!
NOT CONGRUENT
The Congruence PostulatesThe Congruence Postulates
SS S co rr es po nd e nc e
AS A co rre s po nd e nc e
SA S co rr es po nd e nc e
AA S co rre s po nd e nc e
SS A co rr es po nd e nc e
AA A co rre s po nd e nc e
Name That PostulateName That Postulate(when possible)
SASSAS
SASSAS
SASSASReflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSASSA
Let’s PracticeLet’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
∠B ≅ ∠D
For AAS: ∠A ≅ ∠F AC ≅ FE