Coordinate geometry allows us to use the Cartesian plane to analyze geometric shapes. When it comes to triangles, we can verify various properties like side lengths, angles, and whether a triangle is equilateral, isosceles, or right-angled using the coordinates of its vertices. We achieve this by applying formulas such as the distance formula, slope formula, and Pythagorean theorem, all within the coordinate plane.
This worksheet will guide you through using coordinate geometry to prove triangle properties. You'll learn how to calculate side lengths, determine if sides are parallel or perpendicular, and classify triangles based on their properties. Good luck! 📐
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Distance Formula | A. A triangle with all sides of equal length. |
| 2. Slope Formula | B. A triangle with one angle measuring 90 degrees. |
| 3. Equilateral Triangle | C. $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ |
| 4. Right Triangle | D. A line that intersects two or more lines. |
| 5. Transversal | E. $\frac{y_2 - y_1}{x_2 - x_1}$ |
Use the words: coordinates, perpendicular, congruent, isosceles, slope to fill in the blanks.
If two lines are __________, their slopes are negative reciprocals of each other. A triangle with two sides of equal length is called an __________ triangle. To find the length of a side, we need the __________ of its endpoints. Sides of equal length are said to be __________. The __________ of a line segment is essential to determining if two lines are parallel.
Explain how you can use the distance formula and the slope formula together to determine if a triangle defined by three coordinate points is a right triangle.
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