Download More on Triangle congruence

BELL RINGER
Using CPCTC (corresponding parts of
congruent triangles are congruent)…
If Δ HOT ≅ Δ FUN, list the 3 sets of
congruent sides and 3 sets of
congruent angles.
GRAPHIC ORGANIZER
Hypotenuse – the side across from the right
angle in a right triangle
Included – in-between
Non-included – not in-between
Bisect – cut in half (2 congruent parts)
Vertical angles – angles across from each other
when two lines intersect (always congruent).
Reflexive Property – things are congruent to
themselves
VOCABULARY
THE PROBLEM (STRAIGHT FROM DPI)
Andy and Javier are designing triangular gardens
for their yards. Andy and Javier want to
determine if their gardens that they build will
be congruent by looking at the measures of
the boards they will use for the boarders, and
the angles measures of the vertices. Andy and
Javier use the following combinations to build
their gardens.
Will these combinations create gardens that enclose the same area? If so,
how do you know? If not, why?
a. Each garden has length measurements of 12ft, 32ft and 28ft.
b. Both of the gardens have angle measure of 110°, 25° and 45°.
c. One side of the garden is 20ft another side is 30ft and the angle between
those two boards is 40°.
d. One side of the garden is 20ft and the angles on each side of that board
are 60° and 80°.
e. Two sides measure 16ft and 18ft and the non-included angle of the
garden measures 30°.
Let’s think about this…
We’ll answer it a little later.
EXPERIMENT
Using “popsicle
sticks” can you
make 2 triangles
that have the
same angle
measures but are
not congruent?
So, can two
triangles be
congruent by
AAA?
EXPERIMENT
Using just 3
“popsicle sticks”,
can you make 2
non-congruent
triangles that
have 2 congruent
sides and a “nonincluded”
congruent angle?
So, does SSA work
for congruent
triangles?
Will these combinations create gardens that enclose the same area? If so,
how do you know? If not, why?
a. Each garden has length measurements of 12ft, 32ft and 28ft.
b. Both of the gardens have angle measure of 110°, 25° and 45°.
c. One side of the garden is 20ft another side is 30ft and the angle between
those two boards is 40°.
d. One side of the garden is 20ft and the angles on each side of that board
are 60° and 80°.
e. Two sides measure 16ft and 18ft and the non-included angle of the
garden measures 30°.
Now we can answer these.
PRACTICE
Congruent Triangles
Worksheet