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This page shows questions in the Geometry Similarity, Right Triangles, and Trigonometry public release module at MSDE. Geometry
"Geometry Similarity, Right Triangles, and Trigonometry"

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This is a multiple choice question that allows you to select several options.

The figure shows right triangle JLM with segment K M perpendicular to segment J L. Side lengths are given in units.

Right triangle J L M has right angle at M. Side J M is 6 units, side M L is 6 times the square root of 3 units. Angle M is bisected by segment M K, which has length 3 times the square root of 3 units. Triangle K L M has a right angle at K. Side J L is divided into segment J K with length 3 units and segment K L with length 9 units.

For which angles in the figure is the sine equal to one half?

Select all that apply.

  1. A.
    angle J K M
  2. B.
    angle J L M
  3. C.
    angle J M K
  4. D.
    angle J M L
  5. E.
    angle K M L
  6. F.
    angle L J M
  7. G.
    angle L K M

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.

This is a multiple choice question that allows you to select several options.

Parallelogram JKLM is drawn in the coordinate plane. Which transformation must produce a parallelogram that is similar to parallelogram JKLM?

Select all that apply.

  1. A.
    a transformation that doubles the x-coordinates and divides the y-coordinates of each point by 2
  2. B.
    a dilation with scale factor 2 and center J, followed by a dilation with scale factor one third and center L
  3. C.
    a transformation that adds 1 to each x-coordinate and multiplies each y-coordinate by 2
  4. D.
    a dilation with center at the origin and scale factor 3, followed by a reflection over line K M
  5. E.
    a transformation that triples both coordinates of each point

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.

This is a test question that allows you to enter extended text in your response.

Consider triangle R S T, as shown.

Right triangle R S T is shown with angle S marked aa a right angle. Side R T is 15 centimeters. The drawing is not to scale.

In triangle R S T, cosine of R equals three fifths. Find sine of T.

Enter your answer in the box.

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.

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

Quadrilateral JKLM is graphed in the coordinate plane. Under which transformation would the image of JKLM be similar to JKLM?

  1. A.
    coordinates x, y, right arrow coordinates negative 2 x, 2 y
  2. B.
    coordinates x, y, right arrow coordinates negative 3 x, 4 y
  3. C.
    coordinates x, y, right arrow coordinates x plus 5, 5 y
  4. D.
    coordinates x, y, right arrow coordinates y minus 2, 3x

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.