Download 4.2 Apply Congruence and Triangles 4.3 Prove Triangles

Warm-Up
1. What does it mean
for two triangles to
be congruent?
2. If a contractor was
building a house,
how could she or he
check to see if all of
the roof trusses,
which are triangles,
were identical?
Warm-Up
1. What does it mean
for two triangles to
be congruent?
2. If a contractor was
building a house,
how could she or he
check to see if all of
the roof trusses,
which are triangles,
were identical?
4.2 Apply Congruence and Triangles
4.3 Prove Triangles Congruent by SSS
Objectives:
1. To define congruent triangles
2. To write a congruent statement
3. To prove triangles congruent by SSS
Congruent Polygons
Congruent Triangles (CPCTC)
Two triangles are congruent triangles if and
only if the corresponding parts of those
congruent triangles are congruent.
• Corresponding
sides are
congruent
• Corresponding
angles are
congruent
Congruence Statement
When naming two congruent triangles, order
is very important.
Example 1
Write a congruence statement for the
congruent triangles below.
Pay
Attention to
marking
FAT ~ KDI
Example 2
Which polygon is congruent to ABCDE?
ABCDE  -?-
QLMNP
Example 3
U
Locate points I
and S so that
BLUE  FISH.
6
E
4
HINT: use distance an slope to
locate the new points
2
B
S
-5
5
H
-2
-4
F
L
I
Properties of Congruent Triangles
Example 4
What is the
relationship
between <C and
<F?
D
80
F
C
30
They are
corresponding and
congruent
E
A
80
30
B
Third Angle Theorem
If two angles of one triangle are congruent to
two angles of another triangle, then the
third angles are also congruent.
Example 5
Now back to the subject of
roof trusses. Would it be
necessary for the
manufacturer of a set of
trusses to check that all
the corresponding angles
were congruent as well as
the sides?
Answer and explain
in your notebook
Example 5
In other words, is it
sufficient that the
pieces of wood (the
sides of each triangle)
are all the same
length?
Copying a Segment
We’re going to try making two congruent
triangles by simply copying the three sides
using only a compass and a straightedge.
First, let’s learn how to copy a segment.
Copying a Segment
1. Draw segment AB.
Copying a Segment
2. Draw a line with point A’ on one end.
Copying a Segment
3. Put point of compass on A and the pencil
on B. Make a small arc.
Copying a Segment
4.
Put point of compass on A’ and use the compass
setting from Step 3 to make an arc that intersects the
line. This is B’.
Copying a Segment
Click on the
button to
watch a
video of the
construction.
Investigation 1
Now apply the construction for copying a
segment to copy the three sides of a
triangle.
Investigation 1
1. Use your straight edge to construct a
triangle.
2. Now draw a line with A’ on one end.
Investigation 1
3. Copy segment AB onto your line to make
A’B’.
Investigation 1
4. Put point of compass on A and pencil on
C. Copy this distance from A’.
Investigation 1
5. Put point of compass on B and pencil on
C. Copy this distance from B’. This is C’
Investigation 1
6. Finish your new triangle by drawing
segments A’C’ and B’C’.
Side-Side-Side Congruence Postulate
SSS Congruence Postulate:
If the three sides of one triangle are congruent to
the three sides of another triangle, then the two
triangles are congruent.
SSS Congruence Postulate
Example 6
Decide whether the triangles are congruent.
Explain your reasoning.
Answer in your
notebook
Example 7
1. AC ~
= AD
Given
~ BD
BC =
2. AB ~
= AB
Transitive Prop.
~ ABD
3.. ABC =
SSS
Example 8
Explain why the bench with the diagonal
support is stable, while the one without the
support can collapse.