Geometry "Geometry Reasoning" - Public Release

Student Response

Statements	Reasons
B X equals one third open parenthesis B A close parenthesis, B Y equals one third open parenthesis B C close parenthesis	Given
fraction with numerator of B X and denominator of B A equals fraction with numerator of B Y and denominator of B C	Proportions — Substitution one third equals one third
angle B is congruent to angle B	Reflexive Property
triangle BAC is similar to triangle BXY	SAS Similarity
angle BXY is congruent to angle BAC	Corresponding Angles of Similar Triangles are congruent
line segment X Y is parallel to line segment A C	If corresponding angles made by 2 lines cut by a transversal are congruent, then the lines are parallel

Score

Score Point 4

Annotation

This response provides evidence of correct, complete, and appropriate mathematical reasoning. The response is clear and well developed with logical reasoning communicated by the use of precise and appropriate representations, symbols, drawings, or mathematical vocabulary.

The response presents an organized proof with a two-column proof structure as well as logical reasoning to conclude that triangle BAC is similar to triangle BXY using the SAS triangle similarity theorem. From there, the proof uses triangle similarity to identify congruent corresponding angles and explains the converse of the corresponding angles postulate to conclude that line x y is parallel to line A C.

The longer base of a trapezoid has endpoints of coordinates negative 2, negative 4 and coordinates 4, 0 The shorter base contains the point coordinates 3, 1

Coordinate axes are shown with a point plotted at 3, 1 and a line drawn between the points 4, 0 and negative 2, negative 4.

Write an equation of the line that contains the shorter base of the trapezoid. Provide valid mathematical reasoning and calculations to explain how you derived your equation

Enter your equation and your explanation in the space provided.

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In the given diagram

B, X, and A are collinear,

B, Y, and C are collinear, and

B X equals one third open parenthesis B A close parenthesis and B Y equals one third open parenthesis B C close parenthesis

Prove that line X Y and line A C are parallel.

Enter your proof in the space provided.

This page shows questions in the Geometry Reasoning public release module at MSDE. Geometry "Geometry Reasoning"

Icon representing a test question. 1. Year 1, Question 6 (Constructed Response).

Icon representing a test question. 2. Year 1, Question 10 (Constructed Response with Annotations).

This page shows questions in the Geometry Reasoning public release module at MSDE. Geometry
"Geometry Reasoning"