Coordinate Geometry Proofs Challenge

What is the first step in proving that the medians of an isosceles triangle are congruent?

• Find the coordinates of the midpoints

• Use the distance formula

• Find the coordinates of the vertices

• Draw the triangle

After finding the coordinates of the midpoints, what is the next step to prove the medians are congruent?

• Use the distance formula

• Use the slope formula

• Draw a perpendicular bisector

• Calculate the area of the triangle

Why is it necessary to use general coordinates made up of variables to prove the medians are congruent for any isosceles triangle?

• To simplify the calculations

• To represent every possible isosceles triangle

• To avoid using the distance formula

• To make the proof more complex

What is the benefit of using a computer program in coordinate geometry proofs?

• It eliminates the need for calculations

• It replaces the need for a written proof

• It simplifies the proof

• It provides a visual verification of the proof

What is the main advantage of using coordinate geometry proofs over non-coordinate methods?

• They can be easier for some proofs

• They are always easier

• They do not require diagrams

• They are always shorter

In the problem involving a parallelogram, what is given about the diagonals?

• They are parallel

• They bisect each other

• They are congruent

• They are perpendicular

What must be shown to prove that a parallelogram with congruent diagonals is a rectangle?

• The sides are equal

• The angles are right angles

• The diagonals bisect each other

• The diagonals are perpendicular

What is the significance of the coordinates (a + c, b) in the parallelogram problem?

• It represents the midpoint of the diagonal

• It represents the coordinates of the center

• It represents the coordinates of one vertex

• It represents the length of the diagonal

What is the result if the variable 'a' is zero in the parallelogram problem?

• The parallelogram becomes a square

• The parallelogram becomes a line segment

• The parallelogram becomes a rectangle

• The parallelogram becomes a rhombus

What is the final conclusion if the variable 'c' is zero in the parallelogram problem?

• The parallelogram is a square

• The parallelogram is a line segment

• The parallelogram is a rectangle

• The parallelogram is a rhombus