Exploring Proofs with Coordinate Geometry

What is the main difference between lessons 91 and 92?

• Lesson 92 uses concrete numbers.

• Lesson 91 focuses on algebraic expressions.

• Lesson 92 introduces the concept of proofs.

• Lesson 91 covers the mid-segment theorem.

In a coordinate proof, what is the first step you should always take?

• Calculate the slopes.

• Draw and label a diagram.

• Restate the theorem.

• Find the midpoints.

What does the mid-segment theorem of a trapezoid state?

• The mid-segment divides the trapezoid into two equal areas.

• The mid-segment is equal to the length of one base.

• The mid-segment is perpendicular to the bases.

• The mid-segment is parallel to each base and its length is half the sum of the lengths of the bases.

Which formula is used to prove that the mid-segment is parallel to the bases?

• Volume formula

• Area formula

• Slope formula

• Pythagorean theorem

What is the purpose of using the distance formula in the trapezoid mid-segment proof?

• To find the area of the trapezoid

• To find the coordinates of the vertices

• To calculate the perimeter of the trapezoid

• To determine the length of the mid-segment

When planning a proof for the diagonals of a square, what should you show about the slopes of the diagonals?

• They are undefined.

• They are negative reciprocals.

• They are zero.

• They are equal.

What is the final step in writing a coordinate proof?

• Calculate the midpoints.

• Summarize what you have proven.

• Find the slopes.

• Draw the diagram.

Why is it recommended to choose coordinates that make lines horizontal in a coordinate proof?

• To simplify the slope calculations.

• To make the diagram look better.

• To avoid using the distance formula.

• To ensure the lines are perpendicular.

What is a useful tip for choosing coordinates for midpoints?

• Choose coordinates that are divisible by three.

• Choose coordinates that are negative.

• Choose coordinates that are divisible by two.

• Choose coordinates that are prime numbers.

What should you do if the y-axis cuts the figure in half?

• Ignore the y-axis.

• Choose coordinates that cancel each other out.

• Use the x-axis instead.

• Avoid using the y-axis.