Download Congruent Triangles Congruent triangles Proofs

4/17/2012
Congruent triangles
What does congruent mean?
Congruent Triangles
What are the short cuts for proving triangles
congruent?
What are the short cuts for proving right
triangles congruent?
Proofs
In a proof what are some things that could be
given to us to tell us that segments are
congruent?
In a proof what are some things that could be
given to us to tell us that angles are congruent?
What can a figure tell us?
If segment SR and NP bisect each other are the triangles congruent?
S
P
O
N
R
If the triangles are congruent what is your reason?
If Segment SN is parallel to PR and O is the midpoint of segment SR, are the
triangles congruent?
S
If <P = <S and S0 = PO are the triangles congruent?
S
P
O
P
O
N
N
R
If the triangles are congruent, what is the reason?
R
If the triangles are congruent, what is the reason?
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X is the midpoint of AC, And BX is perpendicular to AC, are the triangles congruent?
If triangle ABC is Isosceles with AB = BC and x is the midpoint are the
triangles congruent?
B
B
C
X
A
A
C
X
If the triangles are congruent, what is the reason?
IF the triangles are congruent, what is the reason?
If <A = <C and segment BX bisects < ABC , are
the triangles congruent?
If AD = CB, and AB = CD are the triangles congruent?
A
B
B
D
X
A
If the triangles are congruent, what is the reason?
If ABCD is a rectangle are the two triangles
congruent?
A
C
C
If they are congruent what is the reason?
If AB is parallel to CD are the two triangles congruent?
A
B
B
D
D
C
C
If the triangles are congruent, what is the reason?
If the triangles are congruent what is
the reason?
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If AC and BD bisect each other what triangles are
congruent?
A
If ABCD is a rectangle, is triangle ACD
congruent to triangle BDC?
B
A
B
E
E
D
D
C
C
If the triangles are congruent
what is the reason?
What are the reasons for the triangles to be congruent
Proving Properties
If ABCD is a square, are the four small triangles
congruent?
A
B
E
D
C
• Last unit, we learned that if a quadrilateral has
diagonals that bisect each other, it’s a
parallelogram.
• Let’s prove it:
• Given: Quadrilateral ABCD with diagonals that
intersect at E; AC = BD; E is the midpoint of AC
and BD
If they are congruent what is
the reason?
Draw a picture and mark the given
information
A
B
Proofs
Given Isosceles triangle ABC and BX bisects
angle ABC is triangle ABX congruent to CBX?
E
B
D
C
A
X
C
Sides/Angles Congruent
short cut ______
How do you know ?
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Given the following figure with SN parallel to PR
SR bisects PN. Show: ΔSNO ≅ ΔRPO.
S
Given Isosceles trapezoid ABCD is triangle ABC
congruent to triangle DCB?
P
short cut _________
short cut _____
O
N
R
Sides/Angle congruent
How do you know ?
Sides/angles congruent
How do you know?
HW
Given parallelogram ABCD with diagonal AC
prove that triangle ABC is congruent to triangle
CDA
( draw figure)
short cut ________
Sides/angles congruent
How do you know
1. Given a square ABCD with diagonals AC and
BD which intersect at point E. Prove triangle ABE
is congruent to triangle CBE.
Fold paper in half twice:
You should have 4 sections.
Copy the problem,
Draw a figure , and prove using the same
process as the notes.
2. Given Isosceles trapezoid ABCD whose
diagonals AC and BD intersect at point E. Prove
that triangle AED is congruent to triangle BEC.
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3. Given kite ABCD with diagonals AC and BD
intersecting at E. AC is the shorter diagonal.
Prove that triangle ABE is congruent to triangle
CBE.
4. Given Quadrilateral ABCD with diagonals AC
and BD intersecting at E. If triangle AED is
congruent to triangle CEB, prove that triangle
ABC is congruent to triangle CDA.
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