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Mathematics
9th -
12thgrade
EOC Practice-Transformations, Congruence, and Similarity
20 questions
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- 1. Multiple Choice
Which transformation results in a figure that is similar to the original figure but has a greater area?
A dilation of triangle QRS by a scale factor of 0.25
A dilation of triangle QRS by a scale factor of 0.5
A dilation of triangle QRS by a scale factor of 1
A dilation of triangle QRS by a scale factor of 2
- 2. Multiple Choice
In the coordinate plane, segment PQ is the result of a dilation of segment XY by a scale factor of 1/2. Which point is the center of dilation?
(-4, 0)
(0, -4)
(0, 4)
(4, 0)
- 3. Multiple Choice
The smaller triangle is transformed to create the larger triangle. Which of these is the scale factor of the dilation center at the origin?
4
2
1
1/2
- 4. Multiple Choice
Look at quadrilateral QRST. What is the image of point R after a counterclockwise rotation of 270 degrees about the origin?
(6, -3)
(-3, 6)
(-6, 3)
(3, -6)
- 5. Multiple Choice
Which figure represents the dilation of GH about the origin by a scale factor of 2?
- 6. Multiple Choice
Which transformation of HIJ does NOT result in a congruent triangle?
a reflection across the x axis, followed by a rotation of 180° about the origin
a rotation by 180° about the origin, followed by a translation of 2 units left & 3 down
a translation of 1 unit right and 2 units up, followed by a dilation by a factor of 3
a dilation by a factor of 2, followed by a dilation by a factor of ½
- 7. Multiple Choice
In the triangles shown, ∆ABC is dilated by a factor of 2/3 to form ∆XYZ. Given that m<A=50° and m<B=100°, what is m<Z?
15 degrees
25 degrees
30 degrees
50 degrees
- 8. Multiple Choice
2.0
4.5
7.5
8.0
- 9. Multiple Choice
This is a proof of the statement “If a line is parallel to one side of a triangle and intersects the other two sides at distinct points, then it separates these sides into segments of proportional lengths." Which reason justifies Step 2?
Alternate interior angles are congruent
Alternate exterior angles are congruent
Corresponding angles are congruent
Vertical angles are congruent
- 10. Multiple Choice
Parallelogram FGHJ was translated 3 units down to form parallelogram F’G’H’J’. Parallelogram F’G’H’J’ was then rotated 90° counterclockwise about point G’ to obtain F’’G’’H’’J’’. Which statement is true about parallelogram FGHJ and parallelogram F”G”H”J”?
The figures are both similar and congruent.
The figures are neither similar nor congruent.
The figures are similar but not congruent.
The figures are congruent but not similar.
- 11. Multiple Choice
Consider the triangles shown. Which can be used to prove the triangles are congruent?
SSS
ASA
SAS
AAS
- 12. Multiple Choice
In this diagram, DE is congruent to JI and angle D is congruent to angle J. Which additional information is sufficient to prove that ∆DEF is congruent to ∆JIH?
- 13. Multiple Choice
In this diagram, CD is the perpendicular bisector of AB. The two-column proof shows that AC is congruent to BC. Which theorem would justify step 6?
AAS
ASA
SAS
SSS
- 14. Multiple Choice
In this figure, LN is perpendicular to KM. What additional information would a student need to prove ∆KLN~∆MLN?
- 15. Multiple Choice
In this diagram, STU is an isosceles triangle where ST is congruent to UT. The paragraph proof shows that angle S is congruent to U. Which step is missing in the proof?
CPCTC
Reflexive Property
Definition of right angles
Angle Congruence Postulate
- 16. Multiple Choice
The following is a proof of the Pythagorean Theorem. Which reason justifies step 2?
Triangle proportionality theorem.
Corresponding sides of similar triangles are proportional.
Corresponding sides of similar triangles are congruent.
Triangle mid-segment theorem.
- 17. Multiple Choice
Alternate interior angles are congurent
Corresponding angles are congruent
Vertical angles are congruent
Alternate exterior angles are congruent
- 18. Multiple Choice
Which information is needed to show that a parallelogram is a rectangle?
The diagonals bisect each other.
The diagonals are congruent.
The diagonals are congruent and perpendicular.
The diagonals bisect each other and are perpendicular.
- 19. Multiple Choice
What prove that figure ABCD is a parallelogram?
BD bisects angle ABC.
AB is congruent to AC
BD and AC bisect each other
BD is greater than AC.
- 20. Multiple Choice
This figure shows quadrilateral JKLM. What information will NOT be used to prove that JKLM is a parallelogram?
Show that angle JLM is congruent to angle LJK
Show that JK is congruent to LM
Show that ∆JKL is congruent to ∆LMJ
Show that ∆JKL is congruent to ∆JLM
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