MathBlogGeometryKate

A blog I'm creating for my section 8 Geometry project!

[mathblogkate-blog]

Isosceles Trapezoids....yep more about Trapezoids.

Isocles trapezoids are different because they have congruent (the same measure) legs.

See the bases are still parallel but there are tick marks on the legs show that they have the same measure.

  The corresponding (on the same line) base angles are congruent (same measure) in an isoceles trapezoid, and just like in a normal trapezoid the corresponding leg angles are supplementary (add up to 180). The diagonals in a Isosceles trapezoid  are congruent as well, note the tick marks.

Thats it!

Bib:

http://www.icoachmath.com/Sitemap/images/Isosceles%20Trapezoid2.jpg

http://img.sparknotes.com/figures/B/bc520655c299866d34385c463a8e56f8/isotrap.gif

[mathblogkate-blog]

Trapezoids.

Trapezoids, what art thou?  A trapezoid is a quadrilateral, not a parallelogram, with exactly one pair of parallel sides.

The arrows show that segment BC (in red) is parallel. as is segment AD (in red) The two parallel sides are called the bases. the two sides that aren't labeled with arrows are called the legs. The corresponding (on the same leg) are supplementary (add up to 180)

This image shows the median of a trapezoid, or a segment that connects the midpoints of the two legs. In this example you need to solve for x to find the measure of the two bases and the median. there is a formula for this. M=b1+b2/2 or the median equals base one plus base two divided by 2. just punch the numbers or algebraic statement and you will find your answer. this is due to the fact that the length of the median is half the sum of the bases.  

Thats all folks!

Bib:

http://www.mathwarehouse.com/geometry/quadrilaterals/trapezoid/midsegment/midsegment-theorem.gif

http://www.analyzemath.com/Geometry_calculators/trapezoid_11.gif

[mathblogkate-blog]

Squares?

Let me tell you something about squares. Its a parallelogram with 4 right angles and 4 congruent sides. Here is a picture:

Note the little box in the corner. that means that angles 90 degrees. Its is the same for all the other angles the picture just doesnt label it. The tick marks are showing that all of the sides are congruent.

the diagonals are also congruent in a square. They bisect (cut eachother in half) and are also perpindicular (intersect at 90 degee angles):

  So this picture shows that segment EC is congruent to segment EA and segment BE is also congruent to EC and so is DE. The diagonals bisect the angles they intersect so angle B used to be 90 but is now 45 as are all the angles!

Thats all you need to know!

Bib:

http://www.eserc.stonybrook.edu/glenn/geometry/images/Square.png\

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Rhobi!

A rhombus is a parallelogram with 4 congruent (same measure) sides:

The tick marks show that the sides are congurent.

The rhombus has Perpendicular(intersect at a right angle) Diagonals shown in the picture above and below.

Another feature of the rhombus is that its Diagonals bisect, or cut in half, the angles they intersect.

So say that Angle C, when not bisected is 50 that means angle A is also 50. Then say that B is 130 when not bisected which means D is also 130. Now they are bisected and C and A are 25 and B and D are 65. We all know that a Triangle must add up to 180 so if you put in the perpendicular diagonals and your 4 triangles equal 180.

Thats all folks!

Bib:

http://image.wistatutor.com/content/feed/u385/rhombus_0.GIF

http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/images/rhombus/diagonals/picture2_ccccff.jpg

[mathblogkate-blog]

Rectangles!!!

A rectangle is a paralleogram with four right angles and two pairs of paralell sides:

This is not a rectangle because its angles are not all 90 degrees or right:

The diagonals in a rectangle are congruent (the same measure) like this:

Note the tick marks on the diagonals are all the same showing congruence.

Lets put this in a situation:

If BT=11 then so is TD and AT and TC because they are all congruent. To find AC you would simply add segment AT and segment TC, which gives you 22. Also to solve for the other missing values you take in the fact that the opposing sides of a rectangle are congruent. So if DC=10 so does AB, and if AD=19 so does BC.

Thats it!

Bib:

http://image.wistatutor.com/content/feed/u830/Interior%20angle%20of%20rectangle.PNG

http://01.edu-cdn.com/files/static/learningexpressllc/9781576856918/QUADRILATERAL_WORD_PROBLEMS_05.GIF

http://image.wistatutor.com/content/feed/u762/RECTANGLE.GIF

http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/images/rectangle/diagonal/problem2.jpg

[mathblogkate-blog]

Parallelograms!

 A Parallelogram is a quadrilateral with 2 pairs or parallel sides.

As you can see in the above figure, the opposing sides are congruent, or the same measure, (thats what the little triangles/arrows on the sides mean)

The opposite angles are also congruent:

The consecutive (angle C and angle D is one pair of consecutive as is A+B) are supplementary, or add up to 180. So you would take angle C which is 101.59 and add that too angle D which is 78.41 and that would give you 180.

Diagonals in a parallelogram bisect (split each other in half) each other:

See the marks on the inside lines? that shows that the segment is bisected so that each side is congruent.

Thats all!

Bib:

http://hotmath.com/hotmath_help/topics/diagonals-of-parallelograms/diagonals-of-parallelograms.gif

http://1.bp.blogspot.com/_bMI-KJUhzj4/R1JJwVYDSpI/AAAAAAAABCU/4rAVdoE9rQo/s1600-R/opposite+angles+of+a+parallelogram.JPG

http://www.eserc.stonybrook.edu/glenn/geometry/images/ParallelogramTwoDiagonals.png

[mathblogkate-blog]

Quadrilaterals!!

What is a quadrilateral you say? Well a quadrilateral is a four sided colsed figure whose four angles add up to 360 degrees. Like this

To solve for A here you would add 60+70+135= 265. Then since a quadrilaterals angles add up 360, subtract 265 from 360= 90!

Quadrilaterals can be convex, which is a polygon with all its interior angles less than 180° like this:

 Diagonals, (A line segment drawn from one vertex of a quadrilateral to the opposite vertex),in a Convex quadrilateral intersect, within the quadrilateral.

Or Concave, a polygon with one or more interior angles greater than 180° like this:

Concave quadrilaterals diagonals are outside of the quadrialteral or reflex angles.

This is what they convex and concave look like with diagonals:

A diagonal also connects the non-consecutive, or the angles that don't form a side.

Thats all you need to know!

Bib:

http://image.tutorvista.com/Qimages/QD/18438.gif

"Concave Polygon Definition - Math Open Reference." Table of Contents - Math Open Reference. Web. 14 Feb. 2011. http://www.mathopenref.com/polygonconcave.html.

http://www.tutornext.com/system/files/u27/cq4.JPG

http://www.tutornext.com/system/files/u26/Quad02.gif

 "Convex Polygon Definition - Math Open Reference." Table of Contents - Math Open Reference. Web. 14 Feb. 2011. <http://www.mathopenref.com/polygonconvex.html>.

 http://www.tutornext.com/system/files/u26/Arrowhead.png

"Quadrilaterals." Interactive Maths Series Software (interactive Mathematics Software or Math Software). Web. 14 Feb. 2011. http://www.mathsteacher.com.au/year8/ch09_geometry/07_quad/quad.htm#quad

http://www.btb.gc.ca/images/scolaire-school/fig11.png