8 2 Triangle Sum Theorem

Triangle Sum Theorem Focus - Prove the Triangle Sum Theorem

If you add up the measures of the interior angles of a triangle, What is the total? ,[object Object],25º 65º

How many lines can be drawn through point B that would become parallel to M B

Unique Parallel line Postulate – Through a point not on a given line, there is one and only one line parallel to the given line. m b This postulate will be used in the proof on the next slide.

Given: Prove: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],B C A 2 1 3 D E 4 5

Quadrilateral Theorem ,[object Object],[object Object]

Theorem: Opposite Angles of Quadrilaterals ,[object Object],[object Object]

What can we find out? ,[object Object]

Find the missing angle. ,[object Object]

Find the missing angles. ,[object Object],[object Object],[object Object],Order: y w x

Exterior Angle Theorem ,[object Object],[object Object]

Find the missing angles’ measurements (L and J). ,[object Object],[object Object],J L remote interior angles

What is the measure of Angle U? ,[object Object],[object Object],J L T U To find the measure of angle T, use the definition of supplemental angles. To find the measure of angle U, use the vertical angle theorem.

In today’s lesson we… ,[object Object],[object Object],[object Object]

For Warmup 70° y° z° w° D E 50° x° (x-30)° x° 70° 60° 50° 110° D E 50° 70° (80-30)° 80°

From tdn.com last night. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Want to spend class time preparing for math WASL questions? ,[object Object],[object Object],[object Object],[object Object]

Pg. 446: #17 Proof of Theorem If both pairs of opposite angles of a quadrilateral are equal in measure, then the quadrilateral is a parallelogram.

Given: JKLM is a quadrilateral Prove: JKLM is a parallelogram ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],M J L K statements justifications

Pg. 447: #34 Proof of Theorem An Exterior Angle of a Triangle is equal in measure to the sum of its two remote interior angles.

Given: with exterior Prove: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],C D A B 2 1 3 4 statements justifications

Assignment: pg. 444-448: 14-18a, 26-34, 37-40

8 2 Triangle Sum Theorem

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8 2 Triangle Sum Theorem