Geometry Practice Set

  1. Directions

    Try answering these questions to practice what you have learned about geometry. Answers and explanations follow at the end of the chapter.

  2. Basic

    1. Point m has coordinates (–2, –10), and point n has coordinates (–8, –6). What are the coordinates of the midpoint of the line segment that has endpoints m and n?

    2. The hypotenuse of a right triangle is 17, and one of the legs is 8. What is the area of the triangle?

    3. The area of a circle is 36. What is the circle’s diameter?

    4. Three intersecting lines form triangle XYZ. Interior angle Z is 70 degrees, the angle exterior to Y is 122 degrees, and the vertical to angle X is a degrees.

      In the diagram above, what is the value of a?

    5. Shown is a semicircle circumscribed by rectangle ABCD.

       is the diameter of the semicircle above, which is tangent to . If the area of the semicircle is 50π, then what is the area of rectangle ABCD?

  4. Intermediate

    1. Each side of an equilateral triangle is 12. What is the area of the triangle?

    2. Parallel lines AB and CD intersect parallel lines WX and YZ. Obtuse angle p is formed by the intersection of AB and WX. Acute angle q is formed by the intersection of YZ and CD.

      In the diagram above, . If p = 125°, then what does q equal? 

    3. How many times does the parabola represented by the function  intersect the parabola represented by the function ?

    4. A circle and a square have the same area. What is the ratio of the radius of the circle to the length of a side of the square?

    5. Darnell leaves his house and walks 25 feet due north, then 42 feet due east, and then stops. Melanie leaves the same house and walks 86 feet due east, then walks in a straight line to where Darnell is standing. What is the area of the region enclosed by the paths Darnell and Melanie walked?

  6. Advanced

    1. The perimeter of a rhombus is 44. What is the maximum area the rhombus could have?

    2. The area of circle O is one-fourth that of circle P. The circumference of circle O is what fraction of the circumference of circle P?

    3. Rectangle ABCD is tangent to circle A at point B. Points C and D lie outside the circle. The portion of the rectangle that is not inside the circle is shaded.

      In the figure above, rectangle ABCD is tangent to circle A at point B. If the radius of circle A is 12 and the length of rectangle ABCD is three times its height, what is the area of the shaded region?

    4. Parallelogram ABCD is shown. Angle A is 60 degrees. Side DC contains point F and side AB contains point E. Altitudes DE and BF are drawn.

      In the figure above, DC = 14 and the area of parallelogram ABCD is . What is the area of rectangle EDFB?

    5. Shown is circle O, which is inscribed in square WXYZ.

      In the diagram above, circle O is circumscribed by square WXYZ. Circle O is also the base of a right cylindrical container. When this container is filled with 637π cubic centimeters of liquid, the liquid rises 13 centimeters high. What is the area of square WXYZ, in square centimeters?