Step 2 - Identify which formula we use to prove certain properties of polygons.
Below are properties of triangles/quadrilaterals you’ve been working with closely. Look at the properties given, then match it with the formula you would use to prove it. (Hint: think about the type of answers we expect from each of the formulas listed - use your answers from Step 1 to help!)
**You could use each choice more than once!
_____ 1.) Both pairs of opposite sides are congruent.
_____ 2.) Both pairs of opposite sides are parallel
_____ 3.) Diagonals are congruent.
_____ 5.) Diagonals are perpendicular.
_____ 6.) Sides of polygon create a right angle
_____ 7.) A triangle is isosceles/equilateral.
a.) Midpoint Formula
b.) Slope Formula
c.) Distance Formula
I just need a little help. I'm not asking for the answer, but my teachers aren't responding at the moment. So could somebody give me a few pointers on how to start this? Thank you so SO much. You're a huge help
1c since sides are congruent only if their lengths are equal
2b since parallel lines have the same slope
try the rest
To start solving this problem, let's first understand the properties of triangles and quadrilaterals listed.
1.) Both pairs of opposite sides are congruent: This refers to the property of a parallelogram, where both pairs of opposite sides are of equal length.
2.) Both pairs of opposite sides are parallel: This property also relates to parallelograms, where both pairs of opposite sides are parallel.
3.) Diagonals are congruent: Here, we are talking about the diagonals of a quadrilateral. If the diagonals are congruent, it means that they are of equal length.
5.) Diagonals are perpendicular: Similar to the previous property, we are discussing the diagonals of a quadrilateral here. If the diagonals are perpendicular, it means that they intersect at a right angle.
6.) Sides of the polygon create a right angle: This indicates that the sides of the polygon form a right angle, which is a characteristic of shapes like squares and rectangles.
7.) A triangle is isosceles/equilateral: This property refers to the sides of a triangle. If a triangle is isosceles, it means that at least two sides are of equal length. If it is equilateral, all three sides are of equal length.
Now that we understand the properties, let's associate each property with the appropriate formula:
- To prove that both pairs of opposite sides are congruent (property 1), you would use the Distance Formula (c).
- To prove that both pairs of opposite sides are parallel (property 2), you would use the Slope Formula (b).
- To prove that the diagonals are congruent (property 3), you would use the Distance Formula (c).
- To prove that the diagonals are perpendicular (property 5), you would use the Slope Formula (b).
- To prove that the sides of the polygon create a right angle (property 6), you would use the Slope Formula (b).
- To prove that a triangle is isosceles or equilateral (property 7), you would use the Distance Formula (c).
Remember to carefully refer to each property and think about the expected answers from the listed formulas.