Download Triangles Day 1

Triangles Day 1
SWBAT UTILIZE AND APPLY ORALLY AND IN
WRITING THE THIRD ANGLE CONJECTURE AND
THE TRIANGLE SUM THEOREM TO SOLVE
MISSING ANGLES TO WRITE A BASIC PROOF.
A Proof
Starts from a ‘GIVEN’ piece of information and flows
logically from one reason to the next until it justifies
your conclusion
Listen to Give a Mouse a Cookie twice.
Write five “IF-THEN” statements associated with the
story.
Create your own!
Make up your own proof using on any un- math related topic you want.
Use at least FIVE “IF-THEN” statements.
Example: How I can see a pyramid GIVEN I will go out to eat less
1. If I go out to eat less, then I will save money.
2. If I save money, then I can take a trip.
3. If I go on a trip, then I can go to Egypt.
4. If I go to Egypt, then I can visit the Valley of the Kings.
5. If I see the Valley of the Kings, then I can see a pyramid!
Turn and Share stories with your
neighbor
1. Check to make sure that each
of your stories flows, one
justification into another.
2. Copy your neighbors story
into your notebook as another
example.
3. On a clean piece of paper, pick
the best proof for your group and
write it to be turned in. However,
write it is a paragraph by writing
it one sentence after another!
Insert transition words such as
after, then, next, however, to
make your paragraph sound
right.
Triangle – Definition
A figure formed by the three segments (sides) joining three noncollinear points (vertices)
The symbol for a triangle is ∆.
Use the vertices to name a triangle.
Possible names for this triangle:
∆ABC
∆BCA
∆CAB
∆ACB
∆CBA
∆BAC
Triangle Sum Theorem:
The sum of the measures of the interior angles of a triangle is 180°
m∠𝐴 + m∠B + m∠C = 180°
Corollary to a theorem – a statement that can be proved easily
using a theorem
Corollary to the Triangle Sum Theorem
The acute angles for a right triangle
are complementary
m∠𝐷 + m∠F = 90°
Find the value of x.
84° + 7𝑥 − 5 ° + 8𝑥 − 4 ° = 180°
15𝑥 + 75 = 180
15𝑥 = 105
𝑥=7
B/C it is a right ∆, the two acute angles add up
to 90°
10𝑥° + 19𝑥 + 3 ° = 90°
29𝑥 + 3 = 90
29𝑥 = 87
𝑥=3
Third Angle Conjecture
If two angles of one ∆ are equal in measure to two angles of another
∆ then the third angle in each ∆ are equal to each other.
What is the measure of the
Missing angle in both
triangles?
55°
How could we justify the
Conjecture as a proof?
rd
3
Angle
Complete these blanks:
IF…
Then…
One angle of a right triangle
is 35°
Both shapes are triangles
The other angle measures
______
The sum of the interior
angles measure _____
The equation for the interior
angles is 𝑥 + 35 + 90 = 180
3rd angles are conqruent
Both Δ have a right angle
and a 35° angle
Both angles equal _____
Pg 201 #2
Write an equation for the triangle and solve for x.
Pg 201 #4
Hint* Use what you know about linear angles to help you
Pair Practice
PG 201 #5-9
Use ‘x’ for unknown angles.
Exit Ticket:
The ladder is leaning on the ground at a
75º angle. At what angle is the top of
the ladder touching the building?