Chapter 5 Learning Targets by Lexi Todde

Learning Target #1

atodde303 — 2013-11-12 23:07:46 UTC

I can write indirect proofs. Indirect proofs are proofs that contradict the given information to prove that one thing is true over another. This example from notes helps me to understand these because it clearly shows how to contradict the given to prove something. I am fairly good at these proofs and understand them more than most proofs that I do.

Learning Target #2

atodde303 — 2013-11-12 23:07:53 UTC

I can apply the exterior angle inequality theorem. This is one that I still struggle with and have a hard time understanding. The main idea of this learning target is that when a line is extended from a vertex of a triangle, then the angle created and the angle of the triangle become supplementary.

Learning Target #3

atodde303 — 2013-11-12 23:08:01 UTC

I can use various methods to prove lines parallel. This example from notes helps me because it shows which theorems help prove lines parallel. I understand these concepts very well as they are pretty self explanatory.

Learning Target #4

atodde303 — 2013-11-12 23:08:15 UTC

I can apply the parallel postulate.This says that if there is a point, and a line that is given, any line can be drawn through the point in order to form a line that is parallel to the given one. I understand this and think that it is simple.

Learning Target #5

atodde303 — 2013-11-12 23:08:32 UTC

I can identify pairs of angles formed by a transversal cutting parallel lines. There are about three different types of pairs of angles. They are the alternate interior angles, alternate exterior angles, or corresponding angles. This example helps me to see what each type looks like and where they are located on the diagram.

Learning Target #6

atodde303 — 2013-11-12 23:08:40 UTC

I can apply six theorems about parallel lines. The six theorems are fairly easy to remember and I am confident that I know them all. This example from notes shows their converses, but if you reverse them, you get the original theorem.

Learning Target #7

atodde303 — 2013-11-12 23:08:55 UTC

I can solve crook problems. These are something that I still have trouble with and am still trying to get used to the concept, but basically, the angels that are in the middle and on one side are supplementary and can be figured out that way.

Learning Target #8

atodde303 — 2013-11-12 23:09:04 UTC

I can recognize polygons. Polygons are closed figures with straight edges. The three main types we are learning about are parallelograms, kites, and trapezoids. The other polygons that fall into more specific categories are rectangles, rhombuses, squares, and isosceles trapezoids.

Learning Target #9

atodde303 — 2013-11-12 23:09:15 UTC

I understand how polygons are named. Polygons are named based on the certain properties that they have. For example, a polygon cannot be a square unless it follows the same criteria as a rectangle AND a rhombus.

Learning Target #10

atodde303 — 2013-11-12 23:09:30 UTC

I can recognize convex polygons. Convex angles are angles that have a measure less than 180 degrees. Therefore, convex figures are figures that have angles that are all smaller than 180 degrees.

Learning Target #11

atodde303 — 2013-11-20 19:40:55 UTC

I can recognize diagonals of polygons. Diagonals of polygons are segments that go from non adjacent vertices on a figure. Sometimes they are bisectors of each other and sometimes they are

Learning Target #12

atodde303 — 2013-11-20 19:41:30 UTC

I can identify special types of quadrilaterals. Quadrilaterals can be divided into three main types of figures. There are parallelograms, kites, and trapezoids. In the sub categories there are rectangles, rhombuses, squares, and isosceles trapezoids.

Learning Target #13

atodde303 — 2013-11-20 19:41:51 UTC

I can identify properties of parallelograms, rectangles, kites, rhombuses, squares, and isosceles trapezoids. These are hard concepts to grasp as they are purely memorization and can sometimes be confused with one another, but they are also fairly simple. Each figure has a set of criteria which makes that figure what it is. For example, a parallelogram has opposite angles congruent, opposite sides parallel, and opposite angles congruent.

Learning Target #14

atodde303 — 2013-11-20 19:46:43 UTC

I can prove that a quadrilateral is a parallelogram. A parallelogram has five theorems that are used to prove that figures are indeed parallelograms. These are easy to memorize and are also easy to use in proofs.

Learning Target #15

atodde303 — 2013-11-20 19:47:10 UTC

I can prove that a quadrilateral is a rectangle. A rectangle has three ways to prove that a figure is a rectangle. In order to use the first two theorems listed, one first has to prove that the figure is a parallelogram. As a rectangle is a type of parallelogram, this makes total sense.

Learning Target #16

atodde303 — 2013-11-20 19:47:42 UTC

I can prove that a quadrilateral is a kite. Kites have only two theorems that are used. They are simple and sometimes when a figure is a kite, it can also fall into the category of being a rhombus. This can sometimes get confusing because then a bunch of different theorems are mixing together for the one figure and it is sometimes hard to keep them seperate.

Learning Target #17

atodde303 — 2013-11-20 19:48:02 UTC

I can prove that a quadrilateral is a rhombus. A rhombus is a type of parallelogram and it is also a type of kite. It has three theorems that can be used to prove that a figure is a rhombus. Sometimes, when a figure is a rhombus, it is also a square.

Learning Target #18

atodde303 — 2013-11-20 19:48:27 UTC

I can prove that a quadrilateral is a square. When a quadrilateral is a square, it is also a parallelogram, rectangle, and a rhombus. A square has to have many things in order to be considered a square, and this concept sometimes confuses me.

Learning Target #19

atodde303 — 2013-11-20 19:48:46 UTC

I can prove that a quadrilateral is an isosceles trapezoid. An isosceles trapezoid is a figure that is also a regular trapezoid. This figure has three theorems that can be used to prove it is an isosceles trapezoid. Trapezoids sometimes confuse me. I think that I get confused because we do so few problems with them in it that I am not exactly practiced at solving proofs for them.