Download congruent - Mrs. Durante`s Math Classes

Warm-Up
What are our two definitions of congruent?
1. Two figures that are
the same shape are
congruent if their
corresponding sides
and corresponding
angles are
congruent.
2. Two figures are
congruent if an
isometry or
composition of
isometries maps one
figure onto the other.
Warm-Up
What do isometries preserve?
Angle measures and side lengths.
Using rigid motion transformations and constructions to
show triangles are congruent
Objectives:
1. To define congruent triangles
2. To write a congruent statement
3. To prove triangles congruent by SSS
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
Which polygon is congruent to ABCDE?
ABCDE  -?-
Example 2
U
Locate points I
and S so that
BLUE  FISH.
6
E
4
2
B
S
-5
5
H
-2
-4
F
L
I
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, remember 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’.
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’.
Investigation 1
7. Copy the original triangle ABC onto a
piece of patty paper. Compare this
triangle to triangle A’B’C’. Are they
congruent?
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 3
Decide whether the triangles are congruent.
Explain your reasoning.