Triangles Day 1SWBAT 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 non-collinear 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° mC = 180° Corollary to a theorem – a statement that can be proved easily

using a theoremCorollary to the Triangle Sum TheoremThe acute angles for a right triangle are complementarym = 90°

Find the value of x.

B/C it is a right ∆, the two acute angles add up to 90°

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 3rd Angle Conjecture as a proof?

Complete these blanks:IF… Then…

One angle of a right triangle is 35°

The other angle measures ______

Both shapes are triangles The sum of the interior angles measure _____

Both Δ have a right angle and a 35° angle

The equation for the interior angles is

Both angles equal _____ 3rd angles are conqruent

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?