Ohio State Test Geometry

Triangle ABC has vertices A (1, 1), B (2.5, 3) and C (0,-3). It is dilated by a scale factor of 0.5 about the origin to create triangle A'B'C'. What is the length, in units, side B'C'?

• 3 units

• 3.25 units

• 2.5 units

• 3.75 units

Kyle performs a transformation on a triangle. The resulting triangle is similar to but not congruent to the original triangle. Which transformation did Kyle perform on the triangle?

• Dilation

• Reflection

• Rotation

• Translation

Line segment AB is shown on the coordinate grid. Line segment AB is dilated by a scale factor of 3, with the center of dilation at the origin, resulting in line segment A'B'. What are the endpoints for A'B'?

• A'(-9,0) B' (9,6)

• A'(-9,3) B' (9,6)

• A'(1,1) B' (1,2)

• A'(-2,2) B' (2,-2)

Triangle XYZ is shown. Which triangle must be similar to triangle XYZ?

• A triangle with angles that measure 40 and 60

• a scalene triangle with only one angle that measures 100

• an isosceles triangle with only one angle that measures 40

• a triangle with two angles that measures 40

Circle A is located in the second quadrant with center ( a, b) and radius H. Charlie transforms Circle A to prove that it is similar to any circle centered at the origin with radius G. Which sequence of transformations did Charlie use?

• Translate circle A by ( x + a, y + b) and dilate by a factor of G/H

• Translate circle A by ( x + a, y + b) and dilate by a factor of H/G

• Translate circle A by ( x + a, y - b) and dilate by a factor of G/H

• Translate circle A by ( x + a, y - b) and dilate by a factor of H/G

A park has a triangular sandbox. Todd wants to create a smaller sandbox at his backyard having the same angles as the park sandbox. What is the perimeter, in feet, of Todd's sandbox?

• 52 ft

• 20 ft

• 8 ft

• 20. 8 ft

Which statement is a valid conclusion for Jessica's Proof

• 
• 
• 
• 

• A

• B

• C

• D

• y - 90

• 90 - y

• 90 + y

• -90 +y

What is the missing reason for the seventh statement?

• CPCTC

• AA postulate

• All right triangles are similar

• Transitive property of similarity