**8.10 Pythagorean Theorem; 8.6 Angle Relationships**

__SOLs Covered__:**(28) Triangles; (29) Pythagorean Theorem; (30) Angles; (31) Angle Relationships**

__Math Dictionary Sections__:**Pythagorean Theorem & Angle Relationships Quiz (Mon. 2/4); Quadrilaterals Quiz (Fri. 2/8); Test 3.1 on PT, AR, & Quads (Tues. 2/12)**

__Upcoming Assessments__:Never a dull moment in education or when dealing with technology! Thursday afternoon a coding error was mistakenly sent out to all the county computers that made them almost completely unusable for teachers, thus the delay in this posting as well as the update to grades. Our technology department worked tirelessly over the weekend fixing the server errors as well as driving out to all the county's schools and administrative buildings to manual fix each of the laptops. That's a lot of computers in this county! Thank you to the tech department for your speedy work in getting us back up and running in time for school Monday morning!

Monday was a holiday for students, so when they returned on Tuesday we jumped into our first geometry unit of the year, the Pythagorean theorem. We investigated how the theorem came about using dot paper to try to find the sides of various right triangles. While finding the sides of the shorter two sides (a.k.a. the legs) was fairly simple, finding the longest side (a.k.a. the hypotenuse) required a bit more work, but soon students discovered for themselves that the area of the squares formed off the smaller two sides would together equal the area of the square formed off the longest side, thus giving us the Pythagorean theorem (

*a*² +

*b*² =

*c*²). From that point we worked on various "real world" scenarios where finding the missing side of a right triangle might be necessary.

We then moved onto angles and angle relationships, a concept the students took to very quickly. This topic is much simpler with the new SOLs as middle schoolers are no longer required to learn the angle relationships found in sets of parallel lines intersected by a transversal, but we still spent a little time reviewing how this relates back to the components that are required: complimentary, supplementary, vertical, and adjacent angles. To help students remember the difference between complimentary angles (sets of angles adding up to 90°) and supplementary angles (sets of angles adding up to 180°), I showed them my trick from my days as a student where you can draw a "c" from the 9 in 90° and an "s" on the 8 in 180°. This unit will be wrapped up with a mini-quiz on Monday.

Tangled Web from MangaHigh |

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