geom 5.5 sss and sas
DESCRIPTION
Triangle Similarity Using SSS and SASTRANSCRIPT
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5-5 SSS & SAS
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Proving Triangles Congruent
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Two geometric figures with exactly the same size and shape.
The Idea of a CongruenceThe Idea of a Congruence
A C
B
DE
F
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How much do you How much do you need to know. . .need to know. . .
. . . about two triangles to prove that they are congruent?
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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
E
D
F
1. AB DE
2. BC EF
3. AC DF
4. A D
5. B E
6. C F
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Side-Side-Side (SSS) Similarity Theorem
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
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Side-Side-Side (SSS)Side-Side-Side (SSS)
1. AB DE
2. BC EF
3. AC DF
ABC DEF
B
A
C
E
D
F
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Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
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Side-Angle-Side (SAS)Side-Angle-Side (SAS)
1. AB DE
2. A D
3. AC DF
ABC DEF
B
A
C
E
D
F
included angle
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Slide 1 of 2
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The angle between two sides
Included AngleIncluded Angle
G I H
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Name the included angle:
YE and ES
ES and YS
YS and YE
Included AngleIncluded Angle
SY
E
E
S
Y
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Name That PostulateName That Postulate
SASSAS
SSSSSSSSASSA
(when possible)
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Name That PostulateName That Postulate(when possible)
SASASS
SASSAS
SASASS
Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSSS
AA
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Write a congruence statement for each pair of triangles represented.
A
B
FC
E
D
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ΔACB ΔECD by SAS
B
A
C
E
D
Ex 6
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
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Slide 2 of 2
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Slide 2 of 2
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Slide 2 of 2
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Slide 1 of 2
(over Lesson 5-5)
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Slide 1 of 2
(over Lesson 5-5)