Download Geometry Claims Unit 1: Geometric Structure Geometric structure

Geometry Claims
Unit 1: Geometric Structure
 Geometric structure should be studied outside of the classroom and not inside of the
classroom.
 When solving for x given a segment and its midpoint setting the segments equal to each
other is better than part plus part equals whole.
 In the study of geometry it is more important to know how to solve for a variable in an
equation than it is to evaluate expressions using PEMDAS.
 The best way to find distance on a number line is by using the distance formula rather
than by counting spaces.
 It is better to find distance on a coordinate plane is by using the Pythagorean Theorem
rather than the Distance Formula.
 It is easier to use a protractor than a compass.
 The best foundation for a house is rectangular/triangular/pentagonal.
 A house with more acute/obtuse angles would be more interesting/aesthetically
pleasing/practical to live in.
 Teaching basketball players about angle relationships would improve their shooting
averages.
 When given two points and the y-intercept, the slope intercept formula is more effective
for graphing than the point slope formula.
 The best way to prove two lines are parallel is to check for congruent corresponding
angles/prove they are equidistant/determine the product of their slopes is -1/check for
alternate interior angles/ check for consecutive interior angles.
 A life-sized statue should be sculptured around two parallel poles rather than two
perpendicular poles.
 Parallel lines on playing fields and courts are more effective for measuring distance and
points than perpendicular lines.
Unit 2: Congruence
 Artwork using triangles is more realistic than artwork that does not use triangles.
 When asked to classify a triangle by its sides given coordinates for the vertices, is it
better to graph the triangle and use the Distance Formula than to solve using the
Pythagorean theorem.
 An equilateral triangle would be better than any other triangle for a bicycle frame.
 The best angle for the roof of a house is a/an equilateral/isosceles/scalene triangle.
 The better way to find the missing angle in the example diagram is use the angle sum
and supplement/exterior angle theorem
 It is easier to find a missing angle measure by using the Angle Sum Theorem rather than
the Exterior Angle Theorem.
 When asked to find an angle in an isosceles triangle, the fact sum = 180/ two angles are
equal is more useful.
 20 scalene/ isosceles/ equilateral triangles would make the most attractive quilt pattern
Boston Debate League © 2012
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Before beginning a coordinate proof, it is best to place the figure “on coordinates that
make the computation simple/ so the origin is the center/ so the origin is a vertex/ in the
first quadrant”
The circumcenter/centroid/incenter of a triangle is most applicable to the real world.
___________is the most important example of using triangles to find the distance
between two points.
To determine the measure of each interior and exterior angle of a regular ___ - sided
figure, it is best to use the exterior/interior angle sum first.
All paper should be in the shape of a square/parallelogram/rhombus
It is quickest to determine that a square/rhombus/rectangle is a parallelogram.
Your state should be separated into districts the shape of
parallelograms/triangles/trapezoids/rhombi in order to ensure the most equal coverage.
On a coordinate plane, the best method to prove that a shape is a square is to prove
congruent sides rather than proving intersecting lines are perpendicular.
Unit 3: Similarity
 Similarity should be studied outside of the classroom and not inside of the classroom.
 It is easier/more aesthetically pleasing to create quilts with similar/congruent triangles.
 In a equilateral/right isosceles triangle, it is easier to calculate the length of a missing side
using the properties of a special right triangle/the Pythagorean theorem.
 Rotation/Reflection/Translation is the more useful transformation for furniture movers to
use.
 Triangles/squares/hexagons make the most attractive tessellations for designs.
Unit 4: Two and Three-Dimensional Measurement
 To determine whether a line is tangent to a circle on a coordinate plane, it is better to use
the Pythagorean Theorem/ prove slopes are perpendicular.
 Soccer players would score more goals if soccer fields had more segment markings
within their circular lines.
 To create and explain the parameters of a boundary (for a presidential speech) it is
simpler to use the equations of four lines (2 parallel, 2 perpendicular)/ a circle
 It is better to build a circular/triangular highway around a city.
 Two and Three-Dimensional Measurements should be studied outside of the classroom
and not inside of the classroom.
 It is best to wrap a gift in a box the shape of a prism/cylinder/pyramid/cone/sphere (given
the same surface area).
 The Ancient Egyptians should have built their pyramids in the shape of a hexagonal
pyramid rather than regular square pyramids.
 It is better to measure liquids for cooking in a disposable measuring cup in the shape of a
cone/cylinder.
 It is better to build a kite in the three-dimensional figure of a
prism/cylinder/pyramid/cone/sphere given that the primary purpose of a kite is to catch
wind and stay in the air.
 An ice cream cone should be in the shape of a cylinder rather than a cone.
Boston Debate League © 2012