Geometry Project covering the Following Standards
G.SR.08.03 Understand the definition of a circle; know and use the formulas for circumference and area of a circle
to solve problems.
G.SR.08.04 Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals,
triangles, circles).
G.SR.08.05 Solve applied problems involving areas of triangles, quadrilaterals, and circles.
G.SR.08.06 Know the volume formulas for generalized cylinders ((area of base) x height), generalized cones and
pyramids (1/3 (area of base) x height), and spheres (4/3 (radius)3 ) and apply them to solve problems.
G.SR.08.07 Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids,
and cylinders.
G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids including orthogonal
views (top, front, and side), picture views (projective or isometric), and nets; use such two-dimensional
representations to help solve problems.
G.LO.08.02 Find the distance between two points on the coordinate plane using the distance formula; recognize that
the distance formula is an application of the Pythagorean Theorem.
We Built This City
After landing a big architecture job you are in charge of designing two new buildings for the futuristic
city of Mathematica. As you work with the major, Mr. Euclid, you find out he is very picky about what
His model should contain.
He says it needs:
-Two different three dimensional polyhedrons for the buildings.
-A net drawing of each polyhedral:
*Each net needs to show the number of faces, edges, vertices.
*Name of each polyhedral
*Each Buildings Surface area, and Volume in actual units…NOT MODEL’S UNITS (Show
calculation)
-Floor plan for the rest of the city.
*Needs to have 4 different polygons for other buildings in the floor plan (at least one of which
must be a rectangle)
*Calculation of the distance from one corner to the opposite corner in a floor plan in actual
units.
*Needs to have a scale shown for the model
*Two proportional shadows cast by two different buildings
-Extra paper showing the calculations of the entire area of all two-dimensional buildings in the floor plan
in actual units.
Geometry
Use a ruler and other tools to draw squares, rectangles, triangles, and parallelograms with specified dimensions.
Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an
equilateral triangle, and the bisector of an angle; understand informal justifications.
Understand the concept of similar polygons, and solve related problems
Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are
equal; understand the concepts of similar figures and scale factor.
Solve problems about similar figures and scale drawings.
Show that two triangles are similar using the criteria: corresponding angles are congruent; the ratios of two pairs of
corresponding sides are equal and the included angles are congruent; rations of all pairs of corresponding sides are
equal; use these criteria to solve problems and to justify arguments.
Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor
of r2.
Understand that for polygons, congruence means corresponding sides and angles have equal measures.
Understand the basic rigid motions in the plane (reflections, rotations, translations), relate these to congruence, and
apply them to solve problems.
Understand and use simple compositions of basic rigid transformations.
Construct geometric shapes
Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and
angle bisectors; justify informally.
Geometry Constructions
Fill in the blanks and give examples:
A _____________ is a series of points that extend in two opposite directions without end. You name it
with any two points on it or a lower case letter.
Draw an Example:
A ____________ is part of a line with one endpoint and all the points of the line on one side of the
endpoint. You name it using two points, starting with the end point.
Draw an Example:
A __________ indicates location. It has no size. You name it with a capital letter.
Draw an example:
A __________ is part of a line with two endpoints and all points in between. You name it by its
endpoints.
Draw an Example:
Name each figure:
M
R
Q
R
Parallel lines are in the same plane and never _______.
Intersecting Lines have exactly ______ point in common.
An angle is formed when two _______ have a common endpoint.
A ________ is the intersection of two sides of a figure.
Measure the angles below using a protractor, and label weather they are obtuse, acute, or right below
that (pg 351):
<A=_____________
____________
<ABC =________________
<CDE_____________
________________
_____________
The sum of two complementary angles is ____.
Draw an Example of two complementary angles:
The sum of two supplementary angles is 180o.
Draw an example of two supplementary angles:
Congruent angles are always angle of __________ measure.
________ angles are formed by two intersecting lines, opposite each other, and always congruent.
Identify the pairs of vertical angles to the right:
H.W. Go to thatquiz.org and type the code GERB3155
1
4
2
3
In the figure below ________ is the midpoint of BD . Thus, BM ___ MD . Also, line l is said to be a
_______________ bisector.
l
B
D
_________________ lines intersect to form a 90o andgle.
A segment bisector that intersects it at a 90o angle is said to be a __________________ bisector.
Q: Which line is a perpendicular bisector of segment BD , where M is the midpoint? _________
n
B
q l
m
M
D
A ________ bisector is a ray that divides an angle into two equal angles.
Q Which ray is an angle bisector?_______
B
R
D
T