LN is the perpendicular bisector of KM. LN also bisects KLM, as shown in the diagram below.

What type of triangle must ΔKLM be?

Shannon is making a box. One of the faces, PQRS, is an isosceles trapezoid with the measurements shown below. Shannon wants to put a shelf in the middle to hold plants.

What is the width (w) of the shelf?

In the figure below, line is parallel to line m.

Which of these best describes the relationship between 1 and 2?

Kerry plans to build a picnic table. She needs to create a drawing of the picnic table surface.

Complete the following on a piece of paper and/or in the answer box below:

• Draw a regular hexagon with side lengths of 4 centimeters each. Label the vertices of your hexagon A, B, C, D, E, and F. Label the center of your hexagon O. Explain the steps you used in your drawing.
   
• Classify ΔAOF according to its sides and/or angles. Use mathematics to justify your answers.
   
• Classify ΔABD according to its sides and/or angles. Use mathematics to justify your answer.
   
• Classify ΔABC according to its sides and/or angles. Use mathematics to justify your answer.
   

Which of these regular polygons has an interior angle measuring 120°?

In the figure below, UR is the midsegment of trapezoid PQST.

What is the value of x?

Which of these quadrilaterals has exactly one pair of opposite sides that are parallel?

• Use geometric construction to determine the location of the pool.
   
• Explain the steps you used in your construction. Use words, symbols, or both in your explanation.
   
• Justify that the location you found is equidistant from all three schools.
   

Circle O intersects line m at point P as shown below.

Which of these terms best describes line m?

Lines l and m are parallel and line t is a transversal.

Which pair of angles must be supplementary?

The Department of Public Works wants to put a water treatment plant at a point that is an equal distance from each of the three towns it will service. The location of each of the towns is shown below.

Use the answer box to complete the following. (You will also need to use additional paper to complete the answer satisfactorily.)

• Locate the point that is an equal distance from each of the towns.
   
• Explain how you determined this location. Use words, symbols, or both in your explanation.
   
• Use mathematics to justify your answer.

In the diagram below, points J, M, and L are collinear.

What is the measure of ?

M, P, Q, and R are midpoints of the sides of rectangle WXYZ.

What is the measure of ?

In the figure shown below, lines and are parallel.

What is the value of ?

• Use construction techniques to locate the point where the desk should be.
• Explain the steps you used in your construction. Use words, symbols, or both in your explanation.
• Use mathematics to justify that the location of the desk is equidistant from the walls of the office.

Look at the figure below. Line k is parallel to line l. Line s and line t are transversals that intersect line l at point P.

Which of these statements must be true?

Which of these types of quadrilaterals will always be similar to other quadrilaterals of the same type?

In the figure below,

• S T
   
• RS = 3x; and
   
• RT = 4x - 2.
   

What is the value of x?

Line l is parallel to line m. Line t is a transversal with angle measures as indicated below.

What is the value of x?

Use the segment below to complete each of the following constructions.

Complete the following in the answer box below:

• Using segment AB, construct equilateral triangle ABC. Use mathematics to explain the process you used to construct the triangle. Use words, symbols, or both in your explanation.
   
• Construct circle O so that ΔABC is inscribed in circle O. Use mathematics to explain your process. Use words, symbols, or both in your explanation.
   

Quadrilateral WXYZ is a rhombus, but it is not a square.

Which of these statements is not true?

Circle O is shown below.

Which of these terms best describes MN?