Objective

# Multiple

Choice

# Proofs

1)     Apply the concept of deductive and inductive reasoning to include the following:

a)     Using two and three-dimensional figures, apply postulates, theorems and definitions in writing formal proof through congruent triangles.  (9CI2, C-3)

b)     Sketch an appropriate diagram, state the given information, and state what is to be proved in a given statement.  (9CI2 & J3, C-4)

c)     Apply inductive inquiry to investigate geometric properties and relationships using the geometers sketchpad and/or cabri geometry.  (9I4, C-4)

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2)     Recognize from models and/or appropriately labeled diagrams vocabulary and angle relations

a)     Apply the properties of segments, angles, and their relationships, which include:

b)     the angle bisector; (9AI10, C-2)

c)     right, adjacent, vertical, complementary, and supplementary angles;  (9A, C-1)

d)     “if the exterior sides of two adjacent angles lie in a line, then the angles are supplementary”; (9A, C-2)

e)     “if the exterior sides of two adjacent angles line in perpendicular lines, then the angles are complementary”;  (9A, C-2)

f)      supplements or complements of the same angle are congruent; (9A, C-1)

g)     supplements or complements of congruent angles are congruent.  (9A, C-1)

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3)     Recognize and/or apply properties of triangles and their congruencies including:

a)     a triangle and its parts: vertex, side, interior of a triangle, exterior of a triangle, medians, altitudes, angle bisectors, and perpendicular bisectors of sides; (9AI10, C-2)

b)     given two congruent triangles, state the corresponding congruent parts (CPCTC); (9BI1 & 9CI2, C-2)

c)     given specific information, choose a method of proving triangles congruent from among the following: SSS, SAS, ASA, AAS, HL; (9BI1 & 9CI2, C-3)

d)     “if two sides of a triangle are congruent then the angles opposite theses sides are congruent” and it converse; (9CI1, C-3)

e)     classify triangles according to angles or sides; (9B, C-3)

f)      “The sum of the measures of the three angles of a triangle is ”; (7CI6, C-3)

g)     “The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles”. (7CI6, C-3)

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4)     Given line(s), segment(s), ray(s), plane(s) or combinations thereof, determine and apply parallel and perpendicular relationships.  (9A, C-3)

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5)     Given information about a polygon, determine, where appropriate, any of the following:

a)     type of polygon, (9AI1, C-1)

b)     angle measure(s),  (9AI1, C-2)

c)     side length(s),  (9AI1, C-2)

d)     perimeter,  (9AI1, C-2)

e)     area,  (9AI1, C-2)

f)      apothem,  (9AI1, C-1)

g)     radius.  (9AI1, C-1)

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6)     Given a ratio relating similar polygons and a measure from one (angle, segment length, perimeter or area), calculate the corresponding unknown value.  Given specific information about two polygons, determine if the polygons are similar.  In assessment problems, polygons will be limited to eight or less sides.

      (7CI5, C-4)

a)     Compute unknown lengths or angle measures in right triangles using any of the following:

b)      Pythagorean Theorem,  (9DI1, C-2)

c)     special properties of a 30-60-90 or a 45-45-90 triangle,  (9DI2, C-2)

d)     geometric mean properties,  (9D, C-2)

e)     right triangle trigonometry (sine, cosine, tangent).  (9DI1, C-3)

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7)     Apply the definition and properties of a circle to determine related angle measures, segment lengths, area and circumference.  (C-3,S6D & 9B)

a)     Recognize the following:  circle, radius, diameter, chord, secant, tangent, common internal and external tangents, and internally and externally tangent circles.  (9BI3, C-1)

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8)     Using a compass and straight edge, showing all necessary lines and arcs, complete one or more constructions from the following list:

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9)     Given appropriate information, determine the surface area, volume or unknown segment length in one or more of the following solids (three dimensional figures):

a)     right cylinders;  (7CI6, C-2)

b)     spheres;  (7CI6, C-2)

c)     right triangular or rectangular or hexagonal prisms;  (7CI6, C-2)

d)     cones;  (7CI6, C-2)

e)     right triangular, rectangular or hexagonal pyramids with regular bases.  (7CI6, C-3)

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10)   Apply the formulas for midpoint, slope, distance and circle to given points on the coordinate plane.        (9AI8, C-3)

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11)   Apply geometric concepts to real world situations which include at least two of the following:

a) building constructions;  (9A61, C-4)

b) navigation (land, sea, space);  (9AJ1 & 9AJ3, C-5)

c) surveying (landscaping);  (9AI8, C-5)

d) game (sports/recreation);  (9AI7, C-4)

e) observation of nature. (9AJ3, C-4)

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