int2pd3ch51011

toc = **Chapter 5: Logic and Geometry** = Preview: [|Chapter 5 Preview 1011.pdf]

Wiki Summaries
//**Due the school day after we cover the lesson in class **//

5-1: Denae D. and Olivia G. 5-2: Brandy C. and Tyler E.  5-3: Sarah L. and Sawyer R.  5-4: Hayden B. and Kailyn H.  5-5: Abi M. and Becca S.  5-6: Tanya H. and Keller H.  5-7: Andrew J. and Kayla P.  5-8: Samantha K. and Allison M.  5-9: Derik K. and Ashley U.

**5-1: Elements of Geometry**
Notes: [|Section 5-1 Student 1011.pdf] media type="custom" key="8088750" View the lesson:
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**Student Summaries:**

This lesson basically is the beginning of geometry. A point is a spot anywhere in space and it takes at least 2 points to make a line, and at least 3 points to make a plane. Collinear points lay on the same line, coplanar points are on the same plane. noncollinear points are points that are not on the same line, and noncoplanar points are points that aren't on the same plane. Olivia

This lesson is mostly about starting the process in geometry there are many vocab words in this section some of them are.a line which is a set of points that extend in two directions. A point which is a location of space. The biggest one i think would be Collinear points and noncollinear points and these are when either to points lie on the same line or they do not lie on the same line. -Denae D.

5-2:Angles and Perpendicular Lines
Notes: [|Section 5-2 Student 1011.pdf] media type="custom" key="8100840"

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**Student Summaries:** Tyler E.: this lesson is about angles and perpendicular lines, it describes what degrees are.a degree is what is used to measure an angle, this lesson also teaches us what complementary and supplementary angles are, a complentary angle is foirmed when two angles sums are 90 degrees, a supplementary angle is when two angles have a sum of 180 deegres.

Brandy C.- I learned that there are 2 different angles in a triangle supplementary and complementary supplementary is when the angles equal 180 degrees and complementary is when the angles equal 90 degrees. i learned that perpendicular lines always intersect.

5-3: Parallel Lines and Transversals
Notes: [|Section 5-3 Student 1011.pdf] media type="custom" key="8147566"

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**Student Summaries:** Lesson 5-3 covered the following terms: **Parallel lines**, **Parallel planes**, **Skew lines**, **Transversals**, **Interior angles**, **Exterior angles**, **Alternate exterior angles**, **Same-side interior angles**, **Alternate exterior angles**, and **Corresponding angles**. Also covered throughout this lesson was the rule when dealing with **Parallel line postulates**. Which is; //if two parallel lines are intersected by a transversal then corresponding angles are congruent//. For example if you have a figure with AB ll CD. If m<AEF=(4x+10) degrees and m<EFD=(2x+20) degrees and you need to find m<AEF. You would then need to do the following work to get the answer: work: 4x+10=2x+20 -2x -10x -2x -10x 2x=10 2 2 x=5 by: Sarah and Sawyer

5-4: Properties of Triangles
Notes: [|Section 5-4 Student 1011.pdf]

media type="custom" key="8163444"
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This lesson is about the Properties of Triangles. It tells you how to classify triangles by their sides and angles. There are five properties that will always be true with triangles: 1) The sum of the angles in a triangle is 180 degrees 2) If you add two sides of a triangle, the sum will be bigger than the length of the third side 3) The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle 4) The exterior angle formed at one vertex equals the sum of the other two interior angles 5) If two sides are congruent, then the angles opposite sides are also congruent. - Kailyn H.
 * Student Summaries:**

This lesson is about triangles. Its about obtuse and acute triangles as well as other types of angles. Also it explains the five properties for triangles.-- Hayden B.

5-5: Congruent Triangles
Notes: [|Section 5-5 Student 1011.pdf] media type="custom" key="8210074"

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**Student Summaries:** Lesson 5-5 is about Congruent triangles. It says that two triangles are congruent if their vertices can be matched so that the corresponding parts of the triangle are congruent. This lesson tells us that to show a triangle is congruent you need to that certain combinations of at least three of the corresponding parts are congruent. In this lesson we used 3 postulates: Side-Side-Side postulate (sss), Side-angle-side postulate (sas), Angle-side-angle postulate (asa). Abi

5-6: Quadrilaterals and Parallelograms
Notes: [|Section 5-6 Student 1011.pdf] media type="custom" key="8220966"

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**Student Summaries:** Some Key words you might want to look over are, Quadrilateral, Parallelogram, Opposite Angles, Consecutive Angles, Opposite Sides, and Consecutive Sides. This lesson you should be able to classify different types of quadrilaterals. In this lesson also includes the 7 different properties of a parallelogram. Quadrilateral 4 sides, Parallelogram 2 pair parallel sides, Trapezoid 1 pair parallel sides, Rectangle opposite sides congruent 90 degree angles, Rhombus 4 equal sides, and the Square 4 equal sides 4 90 degree angles. -Tanya H.

Mrs. Tanya has sumed up the chapter very well one thing i would add is the properties. property 1 is opposet sides of a parallelogram are congruent, property 2 is oposet angles of a parelelagram are congruent. Poperty 3 states consecutive angles of a parillelagram are suplimentary. property 4 says the sum of the angle measures of a parallelogram is 360 digrees. and these are the properties of parallelograms. The other three properties are the proporties of diagonals, property 5 and 6 state, diagnols of a parallelogram bisect one another and diagonals of a rectangle are congruent. the last postulate states diagonals of a rhombus are perpendicular. - Keller H.

5-7: Diagonals and Angles of Polynomials
Notes: [|Section 5-7 Student 1011.pdf] media type="custom" key="8292922" View the lesson:
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In this section we talked about the diagonals and angles of polygons. When deciding what equation you should use when you want to find out the measure of one angle or the sum of the angles remember that (n-2)*180 is used to find the sum and you use (n-2)*180/n because you need to divide the sum of the angles by the number of angles in the polygon. Polygons names goes up to 10 and after 10 they are named by n-gon, n meaning the number of sides. The order starts at 3 sides with triangle and increases by one side each time. quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon. Also a polygon can be convex in which if each line is containing a side has no points in the interior of a polygon. Concave is in which a line that contains a side of the polygon also contains a point in its interior. A polygon that has all sides congruent and all angles congruent is called a regular polygon. All of these tools are helpful in finding angle measures and information on polygons for chapter 5-7. Andrew and Kayla!!!!!!!
 * Student Summaries:**

5-8: Properties of Circles
Notes: [|Section 5-8 Student 1011.pdf] media type="custom" key="8293030"

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**Student Summaries:** This lesson studies the properties of circles. This included the definition of a circle as well as knowing the center of the circle. We also learn what a chord is, diameter, minor and major arc as well as determining a semi-circle. We also learn how to find the central angle of a circle. Lastly, we learned about inscribed angles. Allison M.

5-8 explains the properties of circles such as, arc's, minor arc's, major arc's, chord, diameter, radius, semicircle, central angles, and inscribed angles. The arc's determine certain parts of the circle so you can find out the degrees. Ex: If you have a circle and part if it has an angle which would be a minor arc 120 degrees, you would take 360 degrees which is a full circle and subtract 120 from that to get the major arc of the circle. The diameter measures the inside of the circle straight across in the middle. The radius is half of the diameter. Ex: If you have circle with a 12 diameter the radius of that circle would be 6, you divide the diameter by 2 to get that answer. A semicircle is just half of a 360 degree circle so a semicircle is 180 degrees. A chord is a segment where both endpoints are in the circle. A central angle is when the vertex is in the center of the circle. Inscribed angles are when the vertex is on on the circle along with the chords. Samantha K. <3

5-9: Problem Solving Skills: Circle Graphs
Notes: [|Section 5-9 Student 1011.pdf] media type="custom" key="8293034"

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**Student Summaries:** Ashley U.: This lesson is about problem solving skills for circle graphs. Circle Graph- is a visual representation of data where central angles are formed in a circle to show comparisons. Sector- is each part of a circle graph.

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