Download Problem of the Day

Investigation 4.2
AMSTI
Searching for Pythagoras
Problem of the Day
•A
 Using the regular
hexagon, find the total
number of equal
triangles inside. Draw
the triangles from point
A. How many triangles
did you find?
 How many degrees are
in the hexagon?
 How did you find this
answer?
Problem of the Day
•A
 There are six triangles
in a regular hexagon.
 Each triangle is 180°.
 The total number of
degrees in a regular
hexagon is 720°.
 You can use the
formula to find the
answer!
(n – 2)180°
Problem 4.2 (Labsheet 4.2)
A
2
2
C
B
2
 Each side of
equilateral triangle
ABC has a length of
2.
 Remember, all sides
are equal and all
angles are 60°.
Labsheet 4.2
A
C
B
P
 On labsheet 4.2, find the
point halfway between
vertices B and C. Label
this point P.
 Point P is the midpoint of
segment BC.
 Draw a segment from
vertex A to point P.
 This divides triangle
ABC into two congruent
triangles.
Labsheet 4.2
 Cut out triangle ABC
and fold it along line
AP.
 What do you notice
about the two new
triangles?
A
C
B
P
Problem 4.2 (A)
 How does triangle ABP compare with
triangle ACP?
Problem 4.2 (B)
 Find the measure of each angle in
triangle ABP. Explain how you found
each measure.
Problem 4.2 (C)
 Find the length of each side of triangle
ABP. Explain how you found each
length.
Problem 4.2 (D)
 Two line segments that meet at right
angles are called perpendicular line
segments. Find a pair of perpendicular
line segments in the drawing.
Paper Folding
Fold the
corners and
draw a line.
Shade in this
area.
Fold your
paper up the
middle and
draw a line.
Fold the
corners and
draw a line.
Shade in this
area.
Paper Folding
60°
60°
You should have lines like these
drawn on your envelope.
30°
90°
30°
Trace the two
other folds so that
you have two
more lines like
these!
60°
60°
60°
60°
60°
60°
What kind of triangles do you see?
90°
Problem 4.2 Follow-Up (1)
30°
6
60°
 A right triangle with a
60° angle is
sometimes called a 3060-90 triangle. This
30-60-90 triangle has
a hypotenuse of length
6.
 What are the lengths
of the other two sides?
 Explain how you found
your answers.
Problem 4.2 Follow-Up (2)
A
B
D
C
 Square ABCD has
sides of length 1.
 On Labsheet 4.2,
draw a diagonal,
dividing the square
into two triangles.
 Cut out the square
and fold it along the
diagonal.
Problem 4.2 Follow-Up (2)
A
B
D
C
a. How do the two
triangles compare?
b. What are the measures
of the angles of one of
the triangles? Explain.
c. What is the length of
the diagonal? Explain
how you found the
length.
d. Suppose square ABCD
had sides of length 5.
How would this change
your answers to parts b
and c?
ACE Questions for 4.2
Answer the following ACE questions on
page 47 - #2, 4, 7, and 10
Investigation 4.3
AMSTI
Searching for Pythagoras
Investigation 4.3
Special Triangles
For advanced students
or extra enrichment
Special Triangles
 With an equilateral
triangle:
 All sides are equal
(shown by “a”)
 All angles are equal
(60°)
 The perpendicular
bisector is the height
(h) and it creates two
30-60-90 triangles!
4.3
4.3
Special Triangles (30-60-90)


By using a
perpendicular
bisector, the shorter
leg is half of the
hypotenuse. (a/2)
Use this with the
Pythagorean
Theorem to find
missing lengths!
Special Triangles
 This right triangle
is a 45-45-90.
 The two legs are
equal (a).
 The hypotenuse
(h) can be found
by using the
formula h/√a or
the Pythagorean
Theorem.
4.3
Problem (pg 45)
A
60°
C 8
30°
D
B
 If length CD is 8,
what is the length
of AC?
 Now, find the
length of AD.
What length did
you find?
 What is the length
of BC?
 What is the length
of AB?
ACE Problems
#8, 9, 11, 12