6.1: Classifying Quadrilaterals Geometry

Special Quadrilaterals Parallelogram: A quadrilateral with both pairs of opposite sides parallel. Rhombus: A parallelogram with four congruent sides. Rectangle: A parallelogram with four right angles. Square: A parallelogram with four right angles and four congruent sides.

Special Quadrilaterals Kite: A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. Trapezoid: A quadrilateral with exactly one pair of parallel sides. The Isosceles Trapezoid is a trapezoid whose nonparallel opposite sides are congruent.

Classifying Quadrilaterals

Slope and Distance Slope Formula: Distance Formula:

Step 1: Find the slope of each side. Step 2: Use the distance formula to see if any pairs of sides are congruent.

Example 3: Determine the most precise name for quadrilateral ABCD with vertices A(-3,3), B(2,4), C(3,-1), and D(-2, -2).

Example 4:

Example 5: In parallelogram RSTU, 𝑚∠𝑅=2𝑥−10 𝑎𝑛𝑑 𝑚∠𝑆=3𝑥+50. 𝐹𝑖𝑛𝑑 𝑥.