Geometry Placement Test - The Putney School

Geometry Placement TestVocabulary CheckAre you familiar with the following terms? If you are not familiar with a term (or you haveheard of it but do not actually remember what it means) please let us know in the answerform. If English is not your first language please look up these terms in a dictionary; as long asyou know the term in a language you are comfortable with it is okay.point, line, plane, angle, acute, obtuse, right angle, parallel, perpendicular, ray, line segment,polygon, triangle, equilateral triangle, right triangle, isosceles triangle, square, rectangle,rhombus, parallelogram, trapezoid, circle, radius, diameter, circumference, chord (of a circle),secant (of a circle), tangent (of a circle), complementary angles, supplementary angles, vertex(of a polygon), perimeter, area, volume, cylinder, cone, pyramid, sphere, similar, congruent,median (of a triangle), altitude (of a triangle), inscribed circle (of a triangle), circumscribedcircle (of a triangle)Please round all numerical answers to the nearest hundredths.Use the following diagram for problems 1 to 3. In the diagram, the line segments BC and DE areparallel.1. Which of the following statements must be true? Check the box corresponding to thestatement on the answer form if that statement is true. Note that more than one statement inthe list is true.A) The angles ADE and ABC are congruent.B) The measures of angles AED and ABC add up to 90 degrees.C) The polygon BCED is a trapezoid.D) The triangles ABC and ADE are similar.E) The angles ADE and DEC are congruent.2. If the line segment AD measures 3 inches long, BD measures 2 inches long, and CE measures1.5 inches long, find the length of AC in inches. Round your answer to the nearest hundredths.

3. If the angle DAE measures 30 degrees and the angle ADE measures 50 degrees, find themeasure of the angle CED.4. A triangle has sides measuring 8, 25, 30 meters long. Is this a right triangle? Explain youranswer.5. Find the area of the triangle pictured above.6. Find the area of the parallelogram pictured above.7. Given triangles ABC and XYZ with angle A congruent to angle X, side AB congruent to side XYand side BC congruent to side YZ, must triangles ABC and XYZ be congruent? Explain youranswer.

8. Find the area of the kite pictured above.9. Find the perimeter of the kite pictured above. Round your answer to the nearest hundredths.10. Find the circumference of the circle pictured above.11. Find the volume of a cylinder with a radius of 3 and a height of 5.12. Find the shaded area in the circle pictured above.The following diagram is for problems 13 to 15. Point A is the center of the circle shown in thediagram and lines DC and DE are tangent to the circle. Some line segments referred to in the

problems are not shown in the diagram.13. Given that the angle CBE measures 60 degrees, find the angle CDE.14. Given that the angle CBE measures 60 degrees, find the angle CAE.15. Which of the following statements must be true? Check the box corresponding to thestatement on the answer form if that statement is true. Note that more than one statement inthe list is true.A) The line segment AC is perpendicular to line CD.B) The angle CBE is congruent to the angle CDE.C) The circle in the diagram is the inscribed circle of triangle BCE.D) The line segments AB, AC and AE are congruent.E) The line segment CE is congruent to the line segment AD.