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GEOMETRY
Congruent Triangles
HELLO CLASS!
• Students: Please watch this quick video
before beginning this PowerPoint.
Click the Picture
Objectives for Today:
At the end of this PowerPoint you should be
able to
• Accurately recognize that two not similar
figures are not congruent
• Identify corresponding parts of two
congruent triangles with complete
accuracy
• Identify congruent triangles by SSS, SAS,
ASA, or AAS theorems.
• Identify which of the above theorems
proves congruency.
• Recognize that three congruent
corresponding angles does not make
triangles congruent.
CONGRUENCY CHECKLIST
• Figures are congruent if they are:
• The same shape
• The same size
• All corresponding angles are congruent
• All corresponding sides are congruent
But what are corresponding angles and sides?
CORRESPONDING ANGLES AND
SIDES
If ΔDEF was moved on top of ΔGHI,
they would look like one triangle.
Therefore, ∠D and ∠G are corresponding and EF and HI are corresponding
sides.
CORRESPONDING ANGLES AND
SIDES
Sometimes figures have to be rotated or mirrored to find corresponding angles
and sides.
∠D and ∠A are corresponding angles
DF and AB are corresponding sides
THINGS THAT CANNOT BE
CONGRUENT
• Figures that are not the ºsame
shape cannot be congruent.
• Figures that are not the same size
cannot be congruent.
• If not all of the figure’s
corresponding sides and angles are
congruent, then the figures cannot
be congruent.
CONGRUENCY THEOREMS
If all three sides of both triangles are congruent, the triangles are congruent.
SIDE SIDE SIDE
This is called the SSS theorem because:
S
S
S
ide
GH = DE
ide
HI = EF
ide
FD = IG
CONGRUENCY THEOREMS
If two corresponding sides and an angle between them are equal between
two triangles, the triangles are congruent.
SIDE ANGLE SIDE
This is called the SAS theorem because:
S
A
S
ide
ngle
ide
GH = DE
∠G = ∠D
GI = DF
QUESTION ONE
What angles are corresponding?
∠A and ∠E
∠E and ∠B
I’m sorry… but your answer was not correct, please press this button to review
this material. When you are done reviewing, press the button that looks like this
to go back to the quiz.
To Review
CORRESPONDING ANGLES AND
SIDES
Sometimes figures have to be rotated or mirrored to find corresponding angles
and sides.
∠D and ∠A are corresponding angles
DF and AB are corresponding sides
GOOD JOB!!
You chose the correct answer.
Continue
QUESTION TWO
Can these figures be congruent?
No
Yes
I’m sorry… but your answer was not correct, please press this button to review
this material. When you are done reviewing, press the button that looks like this
to go back to the quiz.
To Review
THINGS THAT CANNOT BE
CONGRUENT
• Figures that are not the ºsame
shape cannot be congruent.
• Figures that are not the same size
cannot be congruent.
• If not all of the figure’s
corresponding sides and angles are
congruent, then the figures cannot
be congruent.
GOOD JOB!!
You chose the correct answer.
Continue
QUESTION THREE
Are these figures congruent?
Yes
No
I’m sorry… but your answer was not correct, please press this button to review
this material. When you are done reviewing, press the button that looks like this
to go back to the quiz.
To Review
CONGRUENCY THEOREMS
If all three sides of both triangles are congruent, the triangles are congruent.
GOOD JOB!!
You chose the correct answer.
Continue
ANGLE SIDE ANGLE THEOREM
A
S
A
∠G = ∠D
ngle
ide
ngle
GI = DF
∠I = ∠F
ANGLE ANGLE SIDE THEOREM
A
A
S
ngle
∠G = ∠D
ngle
∠I = ∠F
ide
IH = FE
AAA?
THERE IS NO SUCH THING AS THE ANGLE ANGLE ANGLE THEOREM.
This is why…
Even though all of the angles are congruent,
The figures obviously are not.
A LITTLE EXTRA HELP
• Here is a little song for you guys,
hope you enjoy!
• This website is great for extra
explanation if you guys don’t quite
understand.
• Video on Youtube
• Website
QUESTION FOUR
What theorem proves this congruency?
SSA
SAS
I’m sorry… but your answer was not correct, please press this button to review
this material. When you are done reviewing, press the button that looks like this
to go back to the quiz.
To Review
SIDE ANGLE SIDE
This is called the SAS theorem because:
S
A
S
ide
ngle
ide
GH = DE
∠G = ∠D
GI = DF
GOOD JOB!!
You chose the correct answer.
Continue
QUESTION FIVE
Are these figures congruent?
Yes
No
Maybe So
I’m sorry… but your answer was not correct, please press this button to review
this material. When you are done reviewing, press the button that looks like this
to go back to the quiz.
To Review
AAA?
THERE IS NO SUCH THING AS THE ANGLE ANGLE ANGLE THEOREM.
This is why…
Even though all of the angles are congruent,
The figures obviously are not.
You don’t know this for sure, if any one side is also congruent the figures are
congruent. But you don’t know if a side is congruent or not. So, try again.
Try Again
GOOD JOB!!
You chose the correct answer.
Continue
SUMMARY
These all exist…
• AAA does not!!
THE END
Thanks for watching, here is your homework assignment over this lesson.
Please have it done by tomorrow
Pg 365: Problem 12-50 evens