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INCLUDED??????INCLUDED??????
CA & AR
∠R & ∠C
∠Α IS
INCLUDED
BETWEEN ____
& ____
RC IS INCLUDED
BETWEEN ____
& _____
C
A
R
...
How do we know twoHow do we know two
figures are congruent?figures are congruent?
If all corresponding sides
and angles ar...
Objective:Objective:
To determine ways to
prove triangles
congruent
POSTULATE - SSS POST.POSTULATE - SSS POST.
If three sides of one triangle
are congruent to three sides
of another triangle...
POSTULATE - SAS POST.POSTULATE - SAS POST.
If two sides and the included
angle of one triangle are
congruent to two sides ...
POSTULATE - ASA POST.POSTULATE - ASA POST.
If two angles and the included
side of one triangle are
congruent to two angles...
To determine if triangles are
congruent, what would you
have to measure?
SSS
SAS
ASA
All sides & all angles.
Which postulate, if any, can be used to
prove the triangles congruent?
1. 2.
4.
GT Geometry DrillGT Geometry DrillWrite down the name of the figure described.
Only 1 figure. I will keep giving hints
Hin...
VOCABULARYVOCABULARY
HYPOTENUSE
LEGS
∠D IS A RIGHT
ANGLE
FE IS CALLED THE
___?_______
DF & DE ARE
CALLED ____?____
F
D
E
Geometry ObjectiveGeometry Objective
STW continue to prove
triangle congruent
Given: AB || DC; DCGiven: AB || DC; DC ≅≅ ABAB
Prove: ABC∆Prove: ABC∆ ≅≅ CDA∆ CDA∆
D C
A B
ProofProof
Statement
AC ≅ AC
< BAC ≅ _______
∆ABC ≅ CDA∆
Reason
Given
____________
If _________
____________
____________
Given: RS ST; TU ST; V is theGiven: RS ST; TU ST; V is the
midpoint of STmidpoint of ST
Prove: RSV∆Prove: RSV∆ ≅≅ UTV∆ UTV...
ProofProof
Statement Reason
AAS THEOREMAAS THEOREM
If two angles and a non-included
side of one triangle are
congruent to two angles and a
non-include...
GT GeometryGT Geometry
Given:
Prove:
A
B
C
D
E
F
FEDECBAB ⊥⊥ ; ACFDFEAB ≅≅ ;
FEDABC ∆≅∆
Pythagorean TheoremPythagorean Theorem
a
b
c
Pythagorean TheoremPythagorean Theorem
a
b
c a2
+ b2
= c2
HLTHEOREMHLTHEOREM
If the hypotenuse and a leg of
one right triangle are
congruent to the hypotenuse
and a leg of another ...
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Triangle congruence

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Triangle congruence

  1. 1. INCLUDED??????INCLUDED?????? CA & AR ∠R & ∠C ∠Α IS INCLUDED BETWEEN ____ & ____ RC IS INCLUDED BETWEEN ____ & _____ C A R GEOM Drill 12/17/14GEOM Drill 12/17/14
  2. 2. How do we know twoHow do we know two figures are congruent?figures are congruent? If all corresponding sides and angles are congruent
  3. 3. Objective:Objective: To determine ways to prove triangles congruent
  4. 4. POSTULATE - SSS POST.POSTULATE - SSS POST. If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.
  5. 5. POSTULATE - SAS POST.POSTULATE - SAS POST. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent.
  6. 6. POSTULATE - ASA POST.POSTULATE - ASA POST. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent.
  7. 7. To determine if triangles are congruent, what would you have to measure? SSS SAS ASA All sides & all angles.
  8. 8. Which postulate, if any, can be used to prove the triangles congruent? 1. 2.
  9. 9. 4.
  10. 10. GT Geometry DrillGT Geometry DrillWrite down the name of the figure described. Only 1 figure. I will keep giving hints Hint 1 : I am a special polygon Hint 2: I have three sides Hint 3: I have an angle that is neither obtuse or acute Hint 4: My sides have a special relationship Right Triangle
  11. 11. VOCABULARYVOCABULARY HYPOTENUSE LEGS ∠D IS A RIGHT ANGLE FE IS CALLED THE ___?_______ DF & DE ARE CALLED ____?____ F D E
  12. 12. Geometry ObjectiveGeometry Objective STW continue to prove triangle congruent
  13. 13. Given: AB || DC; DCGiven: AB || DC; DC ≅≅ ABAB Prove: ABC∆Prove: ABC∆ ≅≅ CDA∆ CDA∆ D C A B
  14. 14. ProofProof Statement AC ≅ AC < BAC ≅ _______ ∆ABC ≅ CDA∆ Reason Given ____________ If _________ ____________ ____________
  15. 15. Given: RS ST; TU ST; V is theGiven: RS ST; TU ST; V is the midpoint of STmidpoint of ST Prove: RSV∆Prove: RSV∆ ≅≅ UTV∆ UTV∆ R S T U V ⊥ ⊥
  16. 16. ProofProof Statement Reason
  17. 17. AAS THEOREMAAS THEOREM If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle then the triangles are congruent.
  18. 18. GT GeometryGT Geometry Given: Prove: A B C D E F FEDECBAB ⊥⊥ ; ACFDFEAB ≅≅ ; FEDABC ∆≅∆
  19. 19. Pythagorean TheoremPythagorean Theorem a b c
  20. 20. Pythagorean TheoremPythagorean Theorem a b c a2 + b2 = c2
  21. 21. HLTHEOREMHLTHEOREM If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle , then the triangles are congruent.

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