Question

Match the formula to its use in proving properties of quadrilaterals

midpoint formula
distance formula
slope formula (if opposite reciprocals)
slope formula (if they are equal)
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Answer 1

The formula for proving the properties of quadrilaterals are: 1. Midpoint formula:
`M = \left( \frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2} \right)`. 2. Distance formula:
`d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}}`. 3.
`m_2` =
`-(1)/(m_1)`; 4.
`m_1 = m_2`.

What are the formula used in proving the properties of quadrilaterals?

The properties that is used in proving the properties of a quadrilateral include the following as explained below:

Midpoint formula, which is given as:
`M = \left( \frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2} \right)`.

Distance formula, which is given as:
`d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}}`.

If opposite reciprocals, then the slope formula to use is:
`m_2` =
`-(1)/(m_1)`, where
`m_1` and
`m_2` are the slopes of the two lines.

Where they are equal, the slope formula to use would be:
`m_1 = m_2`.