triangle congruence asa, sss, sas
TRANSCRIPT
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Triangle Congruence
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Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…
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IN ORDER FOR TWO TRIANGLES TO BE CONGRUENT ALL
CORRESPONDING ANGLES AND SIDES MUST BE CONGRUENT!
Congruency Statement ΔABC≅ΔDEF
Based on the congruency statement, which angles and
which sides must be congruent?
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Complete the congruency statement for the following
triangles… ΔPQR≅Δ_______________ ΔPQR≅Δ_______________
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Name the corresponding congruent parts for these triangles.
Corresponding Parts
ABC DEF
1. AB
2. BC
3. AC
4. A
5. B
6. C
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Do you need all six ?
NO !
SSS SAS ASA AAS
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Side-Side-Side (SSS)
1. AB DE
2. BC EF
3. AC DF
ABC DEF
If three sides of one triangle are congruent to three corresponding sides of a second triangle, then the triangles are congruent.
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The angle between two sides
Included Angle
G I H
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Name the included angle:
YE and ES
ES and YS
YS and YE
Included Angle
S Y
E
E
S
Y
The included angle is the angle with the letter that both sides share
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Side-Angle-Side (SAS)
1. AB DE
2. A D
3. AC DF
ABC DEF
included angle
If two sides of one triangle and the included angle are congruent the two corresponding sides and included angle, then the triangles are congruent.
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http://www.youtube.com/watch?v=4GZtALwvRaE&feature=grec_index
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The side between two angles
Included Side
GI HI GH
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Name the included angle:
Y and E
E and S
S and Y
Included Side
S Y
E
YE
ES
SY
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Angle-Side-Angle (ASA)
1. A D
2. AB DE
3. B E
ABC DEF
included side
If two angles of a triangle and the included side are congruent the corresponding angles and included side, then the triangles are congruent.
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Angle-Angle-Side (AAS)
1. A D
2. B E
3. BC EF
ABC DEF
Non-included side
If two angles of a triangle and the non-included side are congruent the corresponding angles and non-included side, then the triangles are congruent.
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Side Names of Triangles
• Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs.
leg
leg
hypotenuse
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Examples: Tell whether the segment is a leg or a
hypotenuse.
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Hypotenuse- Leg (HL) Congruence Theorem:
• If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.
• Example: because of HL.
A X
B C Y Z
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Examples: Determine if the triangles are congruent. State the
postulate or theorem.
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There are 5 ways to prove triangles are congruent…
• Each of these ways have 3 things to look for! – ASA
– SAS
– SSS
– AAS
– HL (Right Triangle)
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Warning: No ASS or SSA Postulate
NO CURSING IN MATH CLASS!
A C
B
D
E
F
NOT CONGRUENT
There is no such
thing as an SSA
postulate!
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Warning: No AAA Postulate
A C
B
D
E
F
There is no such
thing as an AAA
postulate!
NOT CONGRUENT
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The Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
HL correspondence
SSA correspondence
AAA correspondence
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http://www.youtube.com/watch?v=hQYfCWak-Q0
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Name That Postulate
SAS ASA
SSS SSA
(when possible)
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Name That Postulate (when possible)
ASA
SAS
AAA
SSA
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Name That Postulate (when possible)
SAS
SAS
SAS Reflexive Property
Vertical Angles
Vertical Angles
Reflexive Property SSA
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You try! Name That Postulate (when possible)
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(when possible) You try! Name That Postulate
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Let’s Practice
Indicate 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
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You Try!
Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS: