Download Geometry Content Standards Worksheet

Geometry Mathematics Content Standards
Students will:
1.0
Understand undefined terms, axioms, theorems, and inductive and
deductive reasoning
2.0
Write geometric proofs, including proofs by contradiction
3.0
Construct and judge the validity of a logical argument; use
counterexamples to disprove a statement
4.0
Prove basic theorems involving congruence and similarity
5.0
Prove that triangles are congruent or similar, and utilize the
concept of corresponding parts
6.0
Know and be able to use the triangle inequality theorem
7.0
Prove and use theorems involving the properties of parallel lines cut
by a transversal, the properties of quadrilaterals, and the
properties of circles
8.0
Derive and solve problems involving the perimeter, circumference,
area, volume, lateral area, and surface area of common geometric
figures
9.0
Compute the volumes and surface areas of prisms, pyramids, cylinders,
cones, and spheres; and memorize the formulas for prisms, pyramids,
and cylinders
10.0 Compute the areas of polygons, including rectangles, scalene
triangles, equilateral triangles, rhombi, parallelograms, and
trapezoids
11.0 Determine how changes in dimensions affect perimeter, area, and
volume of geometric figures/solids
12.0 Find and use measures of sides and of interior and exterior angles of
triangles and polygons to classify figures and solve problems
13.0 Prove relationships between angles in polygons by using properties of
complementary, supplementary, vertical, and exterior angles
14.0 Prove the Pythagorean theorem
15.0 Use the Pythagorean theorem to determine distance and find lengths of
sides of right triangles
16.0 Perform basic constructions with a straightedge and compass
17.0 Prove theorems by using coordinate geometry
18.0 Know the definitions of the basic trigonometric functions defined by
the angles of a right triangle
19.0 Use trigonometric functions to solve for the sides and angles of a
triangle
20.0 Know and be able to use angle and side relationships in special 3060-90 and 45-45-90 triangles
21.0 Prove and solve problems regarding relationships among chords,
secants, tangents, inscribed angles, and inscribed and circumscribed
polygons of circles
22.0 Know the effect of transformations on figures in the coordinate plane
and space, including rotations, translations, and reflections
NAME_______________________________________ DATE____________________
Geometry Content Standards Worksheet
1.0 Using what you know about parallel
lines cut by a transversal, show that the
sum of the angles in a triangle is the same
as the angle in a straight line, 180
degrees.
2.0 Prove that if two parallel lines are
cut by a transversal, then consecutive
angles are not complementary.
3.0 True or false: A quadrilateral is a
rectangle only if it is a square.
4.0 Prove that if two legs of one right
triangle are congruent to two legs of
another right triangle, then the triangles
are congruent.
5.0
A  X , B  Y , AB  XY prove BC  YZ
6.0 Given a triangle with sides 11 and 17,
between what two values must the length of
the third side be?
7.0 Prove that if the base angles of a
trapezoid are congruent, then the trapezoid
is isosceles.
8.0 An equilateral triangle is inscribed in
a circle of radius 12. Find the difference
of the areas of the these two figures.
9.0 Find the total surface area and volume
of a prism whose base is a regular hexagon
with each side measuring 8 m. and whose
height is 10 m.
10.0 A trapezoid with bases of length 12
and 16 is inscribed in a circle of radius
10. The center of the circle lies inside
the trapezoid. Find the area of the
trapezoid.
11.0 Soap powder is packed in cube-shaped
cartons. A carton measures 10 cm on each
side. The company decides to increase the
length of each edge of the carton by 10
percent. How much does the volume increase?
12.0 A regular polygon has exterior angles,
each measuring 10 degrees. How many sides
does the polygon have?
13.0 Prove that if the diagonals of a
quadrilateral bisect each other, then the
quadrilateral is a parallelogram.
14.0 Prove that for any right triangle, the
sum of the squares of the length of the legs
is equal to the square of the length of the
hypotenuse.
15.0 The bottom of a rectangular box is a
rectangle with a diagonal whose length is
16.0 Construct a 45 degree angle using a
straightedge and compass.
Given triangles ABC and XYZ with
4 3 inches. The height of the box is 4
inches. Find the length of a diagonal of
the box.
17.0 Use a coordinate proof to show that
the median of an isosceles trapezoid has a
length equal to one half the sum of its
bases.
18.0 Without a calculator, determine which
is larger, tan 60 or tan 70 and explain
why.
19.0 In a right triangle, one leg measures
5 cm. The angle opposite the leg is 70
degrees. Find the length of the other leg.
20.0 Each side of the regular hexagon
ABCDEF is 10 cm long. What is the length of
the diagonal AC?
21.0 Two circles, with centers A and B
intersect at points P and Q. Circle A has a
radius of 7 cm and Circle B has a radius of
10 cm. If the length of the common chord PQ
is 8 cm, what is the length of the segment
AB that joins the two radii?
22.0 A translation maps A(2,-3) onto A’(-3,
-5). Under the same translation, find the
coordinates of B’, the image of
B(1, 4).