10/26 WORKBOOK WARM UP Exploring Interior Angles of Triangles– Open your workbooks to P. 351 EXPLORE: A-C!!! Parts A – H.

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Presentation transcript:

10/26 WORKBOOK WARM UP Exploring Interior Angles of Triangles– Open your workbooks to P. 351 EXPLORE: A-C!!! Parts A – H

7.1 INTERIOR & EXTERIOR ANGLES OBJECTIVE I can verify theorems about triangles, including the sum of interior angles. (G.6D)

Triangle Sum Theorem The sum of the interior angles of a triangle is 180. TAKE NOTES

TRIANGLE SUM THEOREM PROOF

STATEMENT REASON 1. Draw line ℓ through point B parallel to A_C . 1. Parallel Postulate 2. m∠1 = m∠ __ and m∠3 = m∠ __ 2. ___________________ 3. m∠4 + m∠2 + m∠5 = 180° 3. Angle Addition Postulate & definition of straight angle 4. m∠ __ + m∠2 + m∠ __ = 180° 4. ____________________ P. 321

EXPLORING INTERIOR ANGLES OF POLYGONS Have students tear out ***check their boxes for orderly books before they leave

POLYGON # OF SIDES # OF TRIANGLES SUM OF INTERIOR ANGLES Triangle 3 1 Quadrilateral 4 2 Pentagon 5 Hexagon 6 Decagon 10 8 P. 352 – 353 PART C - Do you notice a pattern between the number of sides and the number of triangles?

POLYGON ANGLE SUM THEOREM The sum of the measures of the interior angles of a convex polygon with n sides is: (n – 2) 180° Have students complete in workbooks P. 353

I DO, YOU WATCH Determine the unknown angle measures. A) For the nonagon shown, find the unknown angle x°. Have students complete in workbooks P. 354

Determine the unknown angle measures in this pentagon. 6) I DO, YOU HELP Determine the unknown angle measures in this pentagon. 6) Have students complete in workbooks P. 354

P. 355 #S 7 & 8 YOU DO, I HELP Have students complete in workbooks

EXTERIOR & REMOTE ANGLES Exterior Angle – The outside angle of a triangle Remote Angles – Interior angles not adjacent to the exterior angle Have students complete in workbooks P. 354

EXTERIOR ANGLES THEOREM The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Have students complete in workbooks P. 355

EXTERIOR & REMOTE ANGLES Have students complete in workbooks P. 355

REFLECT #9! P. 356 Determine the measure of each exterior angle. Add them together. What can you say about their sum? Explain.

Determine the measure of the specified angle. A) For angle B I DO, YOU WATCH Determine the measure of the specified angle. A) For angle B Have students complete in workbooks P. 357

Determine the measure of the specified angle. B) Find m∠PRS. I DO, YOU HELP Determine the measure of the specified angle. B) Find m∠PRS. Have students complete in workbooks P. 354

P. 358 #S 11 & 12 YOU DO, I HELP Have students complete in workbooks

HW#2: 7.1 P. 360-362 #S 5-15 ODD DUE TOMORROW Have students tear out ***check their boxes for orderly books before they leave