Lesson 11: Polygons and Quadrilaterals Unit Review
Sample Work
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.
____4.) Diagonals bisect each other.
____5.) Diagonals are perpendicular.
____6.) Sides of polygon create a right angle formula.
____7.) A triangle is isosceles/equilateral.
Answers:
A. Midpoint
B. Slope formula
C. Distance
Please help!!
Sure, I'd be happy to help with your review!
Here are the correct answers to match the properties with the corresponding formulas:
1.) Both pairs of opposite sides are congruent - C. Distance
2.) Both pairs of opposite sides are parallel - B. Slope formula
3.) Diagonals are congruent - C. Distance
4.) Diagonals bisect each other - A. Midpoint
5.) Diagonals are perpendicular - B. Slope formula
6.) Sides of polygon create a right angle formula - B. Slope formula
7.) A triangle is isosceles/equilateral - C. Distance
Keep up the great work and remember, just like polygons, you're never too obtuse to learn!
To match each property with the corresponding formula, you'll need to analyze the properties and think about which formula can be used to prove them. Here are the matches:
1.) Both pairs of opposite sides are congruent - C. Distance (The distance formula can be used to calculate the lengths of the sides and determine if they are congruent)
2.) Both pairs of opposite sides are parallel - B. Slope formula (The slope formula can be used to calculate the slopes of the sides and determine if they are parallel)
3.) Diagonals are congruent - C. Distance (The distance formula can be used to find the lengths of the diagonals and determine if they are congruent)
4.) Diagonals bisect each other - A. Midpoint (The midpoint formula can be used to find the midpoint of each diagonal, and if the midpoints are the same, the diagonals bisect each other)
5.) Diagonals are perpendicular - B. Slope formula (The slope formula can be used to calculate the slopes of the diagonals and determine if they are perpendicular)
6.) Sides of the polygon create a right angle - B. Slope formula (The slope formula can be used to calculate the slopes of the sides and determine if any two sides are perpendicular)
7.) A triangle is isosceles/equilateral - C. Distance (The distance formula can be used to calculate the lengths of the sides and determine if they are congruent, proving the triangle is isosceles or equilateral)
So the final matches are:
1.) Both pairs of opposite sides are congruent - C. Distance
2.) Both pairs of opposite sides are parallel - B. Slope formula
3.) Diagonals are congruent - C. Distance
4.) Diagonals bisect each other - A. Midpoint
5.) Diagonals are perpendicular - B. Slope formula
6.) Sides of the polygon create a right angle - B. Slope formula
7.) A triangle is isosceles/equilateral - C. Distance
To match each property with the correct formula, we can consider the information given in the properties and the formulas provided in the answer choices.
1.) Both pairs of opposite sides are congruent: This property relates to the equality of the lengths of opposite sides of a polygon. The formula that can be used to prove this property is the Distance formula (Choice C).
2.) Both pairs of opposite sides are parallel: This property describes the parallelism of opposite sides of a polygon. To prove this, we can use the Slope formula (Choice B), which compares the slopes of the sides.
3.) Diagonals are congruent: This property refers to the equality of the lengths of diagonals within a polygon. The formula that can be used to prove this is the Distance formula (Choice C).
4.) Diagonals bisect each other: This property states that the diagonals of a polygon divide each other into two equal segments. To prove this, we can use the Midpoint formula (Choice A), which helps to locate the midpoint of a line segment.
5.) Diagonals are perpendicular: This property suggests that the diagonals of a polygon are at right angles to each other. We can prove this using the Slope formula (Choice B), which determines whether two lines are perpendicular based on their slopes.
6.) Sides of the polygon create a right angle formula: This property indicates that the sides of the polygon intersect to form right angles. The formula that can be used to prove this is the Distance formula (Choice C).
7.) A triangle is isosceles/equilateral: For this property, which specifically applies to triangles, we do not need to use any of the given formulas. Instead, we can use the properties of isosceles or equilateral triangles to prove it.
Therefore, the correct match between the properties and the formulas is:
1.) Both pairs of opposite sides are congruent: C (Distance)
2.) Both pairs of opposite sides are parallel: B (Slope formula)
3.) Diagonals are congruent: C (Distance)
4.) Diagonals bisect each other: A (Midpoint)
5.) Diagonals are perpendicular: B (Slope formula)
6.) Sides of the polygon create a right angle formula: C (Distance)
7.) A triangle is isosceles/equilateral: No specific formula needed
I hope this helps you with your Unit Review! Let me know if you have any further questions.