Exploring 12 8 Coordinate Proofs

The video tutorial introduces coordinate proofs, explaining how to place geometric figures in a coordinate plane and use variables to represent coordinates. It provides examples with rectangles, triangles, and trapezoids, demonstrating how to calculate side lengths and prove congruence. Advanced techniques and strategies for coordinate proofs are discussed, including the use of the distance and midpoint formulas. The tutorial concludes with tips for avoiding common mistakes and emphasizes the importance of understanding the concepts for future learning.

What is the main purpose of a coordinate proof?

• To draw geometric figures accurately

• To measure angles in geometric figures

• To place geometric figures in a coordinate plane and use variables to represent coordinates

• To find the area of geometric figures

Where should you place one vertex of a shape to easily find the lengths of horizontal and vertical segments?

• At the highest point of the plane

• At any random point

• At the origin (0,0)

• At the midpoint of the plane

In a rectangle placed in a coordinate plane, if one vertex is at (0,0) and the length is h, what are the coordinates of the opposite vertex along the x-axis?

• (h,0)

• (h,h)

• (0,h)

• (0,0)

When placing a right triangle in a coordinate plane, where should the right angle be placed for convenience?

• At the midpoint of the hypotenuse

• At the origin (0,0)

• At the highest vertex

• At any random point

In an isosceles trapezoid, if the length of one side is c, what is the total length of the base if the other side is also c?

• c

• 4c

• 2c

• c/2

What is the reflexive property used for in coordinate proofs?

• To show that a line segment is perpendicular

• To show that a line segment is congruent to itself

• To show that a line segment is parallel

• To show that a line segment is longer than another

Which theorem can be used to prove that two triangles are congruent if they have two equal sides and the included angle is equal?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

What is the distance formula used for in coordinate geometry?

• To find the midpoint of a line segment

• To find the slope of a line

• To find the area of a triangle

• To find the length between two points

If the coordinates of point P are (0,k) and point Q are (k,0), what is the distance between P and Q?

• k

• k^2

• sqrt(2k)

• sqrt(k^2 + k^2)

Why can't the area alone be used to prove that two geometric figures are congruent?

• Because area only applies to rectangles

• Because area is difficult to calculate

• Because area does not account for shape and angles

• Because area is not a reliable measure