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

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The figure shows quadrilateral RSUV with segment R V parallel to segment S U and congruent segments as marked.

Quadrilateral RSUV is shown with diagonals. The diagonal between R and U is labeled K. Segment RV and segment SU are marked as congruent.

Prove that segment R U bisects segment S V by placing the reasons for steps 4 and 5 in the proof.

4) Angle Angle Angle 4) Angle Side Angle 4) Side Side Side 5) Corresponding sides of similar triangles are congruent. 5) Corresponding sides of congruent triangles are congruent.
Statement Reason
1) Quadrilateral RSUV with segment R V parallel to segment S U and segment R V congruent to segment S U 1) Given
2) angle K S U is congruent to angle K V R 2) Alternate interior angles formed by parallel lines cut by a transversal are congruent.
3) angle S U K is congruent to angle K R V 3) Alternate interior angles formed by parallel lines cut by a transversal are congruent.
4) triangle S U K is congruent to triangle V R K
5) segment S K is congruent to segment V K
6) segment R U bisects segment S V 6) Definition of bisect

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This is a multiple choice question that allows you to select only one option.

The figure shows rectangle PQRS in the first quadrant of a coordinate plane.

Coordinate axes are shown. Quadrilateral QRPS is shown in the first quadrant. Q is at point x 1, y 2. R is at point x 2, y 2. S is at point x 2, y 1. P is at point x 1, y 1.

Rectangle PQRS is reflected across the x-axis. The image is p prime q prime r prime s prime. Which two further transformations will carry rectangle p prime q prime r prime s prime. back onto rectangle PQRS?

  1. A.
    reflection across the y-axis followed by a reflection across the x-axis
  2. B.
    reflection across the y-axis followed by a reflection across the line with equation y equals the opposite of x
  3. C.
    reflection across the y-axis followed by a 180° rotation around the origin
  4. D.
    reflection across the line with equation y equals x followed by a 180° rotation around the origin

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.