Question

match the formula that goes with the given characteristic. sides or diagonals are congruent sides or diagonals are perpendicular diagonals bisect sides are parallel drag & drop the answer midpoint formula slope formula distance formula or pythagorean theorem

Explanation:

Step1: Analyze "Sides or diagonals are congruent"

To check if sides or diagonals are congruent, we need to find the length between two points. The Distance Formula ($d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$) or the Pythagorean Theorem (which is related to finding lengths in right triangles, and can be used to find the length of sides/diagonals) is used to find the length. So "Sides or diagonals are congruent" matches with "Distance Formula or Pythagorean Theorem".

Step2: Analyze "Sides or diagonals are perpendicular"

To check if two lines (sides or diagonals) are perpendicular, we check the slopes. If the product of the slopes of two lines is -1, they are perpendicular. The Slope Formula ($m=\frac{y_2 - y_1}{x_2 - x_1}$) is used to find the slope of a line. So "Sides or diagonals are perpendicular" matches with "Slope Formula".

Step3: Analyze "Diagonals bisect"

If diagonals bisect each other, the midpoint of both diagonals is the same. The Midpoint Formula ($M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$) is used to find the midpoint of a line segment. So "Diagonals bisect" matches with "Midpoint Formula".

Step4: Analyze "Sides are parallel"

To check if two sides are parallel, we check the slopes. If the slopes of two lines are equal, they are parallel. The Slope Formula ($m=\frac{y_2 - y_1}{x_2 - x_1}$) is used to find the slope of a line. So "Sides are parallel" matches with "Slope Formula"? Wait, no. Wait, parallel lines have equal slopes. So to check if sides are parallel, we use the Slope Formula to find the slopes of the sides and see if they are equal. Wait, but let's re - check:

Wait, for "Sides are parallel": The slope formula is used to find the slope of each side. If the slopes are equal, the sides are parallel. So "Sides are parallel" matches with "Slope Formula"? Wait, no, let's correct:

Wait, let's re - assign:

1. Sides or diagonals are congruent: Distance Formula or Pythagorean Theorem (because we need to find the length to check congruence)
2. Sides or diagonals are perpendicular: Slope Formula (because the product of slopes of perpendicular lines is - 1, so we use slope formula to find slopes)
3. Diagonals bisect: Midpoint Formula (because bisecting means the midpoint of both diagonals is the same, so midpoint formula is used)
4. Sides are parallel: Slope Formula (because parallel lines have equal slopes, so we use slope formula to find slopes and check if they are equal)

Wait, but let's confirm:

• Congruent (same length): Distance Formula or Pythagorean Theorem (correct, as distance formula gives the length between two points)
• Perpendicular (slopes multiply to - 1): Slope Formula (correct, as slope formula gives the slope of the line)
• Diagonals bisect (same midpoint): Midpoint Formula (correct, as midpoint formula gives the midpoint of a segment)
• Sides are parallel (equal slopes): Slope Formula (correct, as slope formula gives the slope, and equal slopes mean parallel lines)

Answer:

• Sides or diagonals are congruent: Distance Formula or Pythagorean Theorem
• Sides or diagonals are perpendicular: Slope Formula
• Diagonals bisect: Midpoint Formula
• Sides are parallel: Slope Formula