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Geometry District Benchmark

Starting Dates Block Spr None Mar 16th Nov 12th May 18th Notes
  Block Fall None Oct 13th Mar 16th Jan 5th  
  Traditional Oct 13th Jan 5th Bmk 3 May 18th  
Geometry Star Bmk 1 Bmk 2   Bmk 4  
Logic and Geometric Proofs 22.67 17 24 20 19  
1.0* Students demonstrate understanding by identifying and giving examples of
undefined terms, axioms, theorems, and inductive and deductive reasoning
2 3 1 1 1  
2.0* Students write geometric proofs, including proofs by contradiction. 3 4 3 2 2  
3.0* Students construct and judge the validity of a logical argument and give
counterexamples to disprove a statement.
4 4 4 3 3  
4.0* Students prove basic theorems involving congruence and similarity. 5   6 5 4  
5.0 Students prove that triangles are congruent or similar, and they are able to
use the concept of corresponding parts of congruent triangles.
2   3 3 3 2: no Similar
6.0 Students know and are able to use the triangle inequality theorem. 1   2 2 1  
7.0* Students prove and use theorems involving the properties of parallel lines
cut by a transversal, the properties of quadrilaterals, and the properties of circles.
5.67 6 5 4 5 1/2: No Circles or
Quads
Total Items 22.67 17 24 20 19  
Percent 35% 77% 59% 45% 32%  
Volume and Area Formulas 11 0 0 0 10  
8.0* Students know, derive, and solve problems involving perimeter,
circumference, area, volume, lateral area, and surface area of common geometric
4       2  
10.0* Students compute areas of polygons, including rectangles, scalene
triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
4       3  
9.0 Students compute the volumes and surface areas of prisms, pyramids,
cylinders, cones, and spheres; and students commit to memory the formulas for
prisms, pyramids, and cylinders.
2       3  
11.0 Students determine how changes in dimensions affect the perimeter, area,
and volume of common geometric figures and solids.
1       2  
Total Items 11 0 0 0 10  
Percent 17% 0% 0% 0% 17%  
Angle relationships, constructions and lines 16.33 5 12 13 14  
12.0* Students find and use measures of sides and of interior and exterior angles
of triangles and polygons to classify figures and solve problems.
5   5 5 4  
13.0 Students prove relationships between angles in polygons by using properties
of complementary, supplementary, vertical, and exterior angles.
2   3 2 3  
14.0* Students prove the Pythagorean theorem. 0.33          
15.0 Students use the Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles.
2   0 2 3  
16.0* Students perform basic constructions with a straightedge and compass,
such as angle bisectors, perpendicular bisectors, and the line parallel to a given
line through a point off the line.
4 5 2 2 2 1: No Perp Bisect or
line par to pts
17.0* Students prove theorems by using coordinate geometry, including the
midpoint of a line segment, the distance formula, and various forms of equations
of lines and circles.
3   2 2 2 2:No Circles
Total Items 16.33 5 12 13 14  
Percent 25% 23% 29% 30% 23%  
Trigonometry 15 0 5 11 17  
18.0* Students know the definitions of the basic trigonometric functions defined
by the angles of a right triangle. They also know and are able to use elementary
relationships between them. For example, tan(x ) = sin(x )/cos(x ), (sin (x ))2 +
(cos (x ))2 = 1
3     3 3  
19.0* Students use trigonometric functions to solve for an unknown length of a
side of a right triangle, given an angle and a length of a side.
3     3 3 Cluster: TRIG
20.0 Students know and are able to use angle and side relationships in problems
with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and
90° triangles.
1     3 3  
21.0* Students prove and solve problems regarding relationships among chords,
secants, tangents, inscribed angles, and inscribed and circumscribed polygons of
circles.
5       5  
22.0* Students know the effect of rigid motions on figures in the coordinate plane
and space, including rotations, translations, and reflections.
3   5 2 3  
Total Items 15 0 5 11 17  
Percent 23% 0% 12% 25% 28%  
TOTAL 65 22 41 44 60