# Geometry Practice Questions

Geometry questions are very common on high school exit exams, some nursing entrance exams, and college entrance exams. Topics vary, but most of the following are covered:

– identifying solid figures

– solving problems with solid and plane figures

– solving problems using Pythagorean principles

– solve problems using scale drawings

– calculating area, circumference, volume and perimeter

– solve problems using geometric transformations

**1. Which of the above points represents the origin?**

- A
- B
- C
- D

**2. What is measurement of the indicated angle?**

- 45
^{o} - 90
^{o} - 60
^{o} - 30
^{o}

**3. What is perimeter of the above shape?**

- 12 cm
- 16 cm
- 6 cm
- 20 cm

**4. What is (area of large circle) – (area of small circle) in the figure above?**

- 8 π cm
^{2} - 10 π cm
^{2} - 12 π cm
^{2} - 16 π cm
^{2}

**5. What is the length of each side of the indicated square above?**

- 10
- 15
- 20
- 5

**6. Which of the lines above represents the equation 2y – x = 4?**

- A
- B
- C
- D

**7. What is the measurement of the indicated angle?**

- 45
^{o} - 90
^{o} - 60
^{o} - 50
^{o}

# Answer Key

**1. A**

Point A represents the origin.

**2. B** The diagonals of a square intersect perpendicularly with each other so each angle measures 90

^{o}x =90

^{o}

**3. B** The square with 2 cm side common to the rectangle apart from 4 cm side. So the perimeter = 2+2+2+4+2+4 = 16 cm

**4. C** Given: Two circles with smaller circle (diameter given) exactly half the larger circle (radius given).

Difference = (Area of large circle) – (Area of small large circle)

π 4

^{2}– π 2

^{2}= 16π

^{ }– 4π

Difference = 12π cm

^{2}

**5. B**

**Pythagorean Theorem:**

(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2} h^{2} = a^{2} + b^{2}

a^{2} = 81, b^{2} = 144

h^{2} = a^{2} + b^{2} h^{2} = 81+144

h^{2} = 225

h= 15

**6. A**

Line A represents the equation 2y – x = 4.

**7. C** The sum of angles around a point is 360

^{o}d+300 = 360

^{o}d = 60

^{o}

# Geometry Tutorials

**Euclidean geometry** (Wikipedia)

High School Geometry Tutorials (About.com)

Teaching High School Geometry – An excellent article about teaching geometry from HomeSchoolMath