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Sample Praxis Geometry Practice Questions
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1Two triangles are congruent by SAS if which of the following is true?
A.Two sides and the included angle of one triangle equal the corresponding parts of the other
B.Three angles of one triangle equal three angles of the other
C.Two angles and a non-included side are equal
D.The triangles have equal perimeters
Explanation: SAS (Side-Angle-Side) congruence requires two sides and the angle BETWEEN them (the included angle) to be equal to the corresponding parts of the other triangle. This guarantees the triangles are identical. AAA only proves similarity, not congruence.
2A rigid motion (isometry) is a transformation that preserves which property?
A.Only orientation
B.Distance between points
C.Area but not shape
D.Color and shading
Explanation: A rigid motion (translation, rotation, reflection) preserves distances between all points, which means it preserves lengths, angle measures, and overall size and shape. The image is congruent to the original figure.
3Triangle ABC has angles measuring 40 and 75 degrees. What is the measure of the third angle?
A.115 degrees
B.75 degrees
C.65 degrees
D.45 degrees
Explanation: The angles of a triangle sum to 180 degrees. So the third angle = 180 - 40 - 75 = 65 degrees.
4Which transformation maps a point (x, y) to (x, -y)?
A.Translation down 2 units
B.Reflection across the y-axis
C.Rotation of 90 degrees
D.Reflection across the x-axis
Explanation: Reflecting across the x-axis keeps the x-coordinate the same and negates the y-coordinate, giving (x, -y). Reflection across the y-axis would instead produce (-x, y).
5Two triangles are congruent by the HL theorem when which condition is met?
A.The hypotenuse and one leg of two right triangles are equal
B.Two legs of two right triangles are equal
C.The hypotenuse and an acute angle are equal
D.Two angles of two right triangles are equal
Explanation: The HL (Hypotenuse-Leg) theorem applies only to right triangles: if the hypotenuse and one leg of one right triangle equal the hypotenuse and corresponding leg of another, the triangles are congruent. The right angle plus these two sides fixes the triangle.
6A point is rotated 90 degrees counterclockwise about the origin. If the original point is (3, 1), what is the image?
A.(1, -3)
B.(-1, 3)
C.(-3, -1)
D.(3, -1)
Explanation: A 90-degree counterclockwise rotation about the origin maps (x, y) to (-y, x). For (3, 1) this gives (-1, 3).
7In triangle ABC, AB = AC. If angle B = 50 degrees, what is angle A?
A.100 degrees
B.50 degrees
C.80 degrees
D.65 degrees
Explanation: Since AB = AC, the triangle is isosceles and the base angles B and C are equal, so angle C = 50 degrees. Then angle A = 180 - 50 - 50 = 80 degrees.
8Which of the following is NOT a rigid motion?
A.Rotation about a point
B.Reflection across a line
C.Translation by a vector
D.Dilation with scale factor 2
Explanation: A dilation with scale factor 2 changes the size of a figure, so it does not preserve distances and is not a rigid motion. Translations, reflections, and rotations all preserve distance and are rigid motions.
9Two parallel lines are cut by a transversal. If one of the co-interior (same-side interior) angles is 110 degrees, what is the other?
A.70 degrees
B.110 degrees
C.20 degrees
D.250 degrees
Explanation: Co-interior (same-side interior) angles formed by a transversal cutting parallel lines are supplementary, summing to 180 degrees. So the other angle = 180 - 110 = 70 degrees.
10The composition of two reflections across two parallel lines is equivalent to which single transformation?
A.A rotation
B.A translation
C.A dilation
D.A glide reflection
Explanation: Reflecting across two parallel lines produces a translation perpendicular to the lines, with distance equal to twice the distance between the lines. Reflections across two intersecting lines instead produce a rotation.
About the Praxis Geometry Practice Questions
Verified exam format metadata for Praxis Geometry (5163) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.