Download Triangles

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Triangle Congruences
Day 2
+ Warm Up 1
1.
9.8.2014
Find the missing angles below
y
70
x
70
40
40
2. Use Pythagorean Theorem to find the missing side
d
4
3
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Essential Question #9
How
can we prove triangles are
congruent?
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Today’s Objective
 Use
triangle congruence postulates and
theorems to prove that triangles are
congruent.
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Proving Triangles Congruent
 By
the definition of Congruence, what do
we need to show to prove two triangles are
congruent?
 All
corresponding angles are congruent
 All corresponding sides are congruent
 That’s
 With
six pairs!
Triangles, we have postulates that
allow us to only need to show three pairs,
but they have to be in a specific order
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If the three sides of one triangle are
congruent to the three sides of another
triangle, then the two triangles are
congruent.
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If two sides and the included (between) angle
of one triangle are congruent to two sides and
the included angle of another triangle, then
the two triangles are congruent.
+ Non-example of SAS:
Why can’t we use SAS to show
these triangles are congruent?
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If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, then the two
triangles are congruent.
+ We now have the following:
 SSS
– side, side, side
 SAS
– Side, Angle (between), Side
 ASA
– Angle, Side (between), Angle
+ Examples
Which Theorem proves the Triangles are congruent?
1.
+ Sometimes we have to mark
Assumptions!
Assumption #1: Reflexive Property
 If
two triangles share a side, that side is
congruent to itself
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What do we know about the third
angle if two are congruent?
2.
+ Assumption #2: Third Angle
 If
two pairs of corresponding angles are
congruent, then the third pair is also
congruent!
 Why? Triangle
Angle Sum Theorem says
the measures of the angles have to sum to
180!
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What do we know about vertical
angles?
3.
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Assumption #3: Vertical Angles
Vertical Angles are Congruent!
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4.
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Assumption #4: Third Side of a
RIGHT Triangle
 If
two pairs of corresponding sides are
congruent in a RIGHT TRIANGLE, then the
third pair is also congruent!
 Why?
Pythagorean Theorem states that
a2+b2=c2. This can only be true if a, b, and c
are the same in both triangles
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Additional Examples
5.
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Additional Examples
6.
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Exit Ticket - Worksheet
HOMEWORK - Worksheet