Geometry: Polygons and Quadrilaterals

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Questions and Answers

What is the formula for the sum of one interior angle?

(n-2)180/n

How do you find the number of sides of a polygon based on the sum of its interior angles?

(n-2)180 = sum of interior angles

How do you find an unknown interior or exterior angle?

Set it equal to 360

What is a parallelogram?

A quadrilateral with both pairs of opposite sides parallel Signup and view all the answers

How do you find the point of intersection in a parallelogram?

Use the midpoint formula on the coordinates of a diagonal angle Signup and view all the answers

What is the midpoint formula?

(x₁+x₂)/2, (y₁+y₂)/2 Signup and view all the answers

How do you find the coordinates of a point given the coordinates of others?

Find the slope of two points and apply it to the other point to find the coordinate. Signup and view all the answers

How do you identify a parallelogram in the coordinate plane?

Use the distance formula to prove congruency and the slope formula to prove parallel. Signup and view all the answers

What is the slope formula?

m = (y₂ - y₁)/(x₂ - x₁) Signup and view all the answers

What is the Distance Formula?

d = √[(x₂ - x₁)² + (y₂ - y₁)²] Signup and view all the answers

What is a rhombus?

A parallelogram with 4 congruent sides Signup and view all the answers

What is a rectangle?

A quadrilateral with four right angles Signup and view all the answers

What is a square?

A parallelogram with four congruent sides and four right angles Signup and view all the answers

What are the characteristics of a rhombus?

Diagonals are perpendicular and diagonals bisect a pair of opposite angles Signup and view all the answers

What are the characteristics of a rectangle?

Diagonals are congruent Signup and view all the answers

What are the characteristics of a square?

Diagonals are perpendicular and diagonals are congruent Signup and view all the answers

What is a trapezoid?

A quadrilateral with exactly one pair of parallel sides Signup and view all the answers

What are trapezoid base angles?

Two consecutive angles whose common side is a base Signup and view all the answers

What are the legs of a trapezoid?

Nonparallel sides Signup and view all the answers

How do you identify a trapezoid in the coordinate plane?

Use slope for opposite sides to see if parallel and check if legs are congruent with distance formula. Signup and view all the answers

What is the mid segment of a trapezoid?

1/2(b₁ + b₂) Signup and view all the answers

What is a kite?

A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent Signup and view all the answers

What are the characteristics of a kite?

One pair of opposite angles are congruent and its diagonals are perpendicular Signup and view all the answers

How do you find a rectangle on a coordinate plane?

Find the slope of both pairs of opposite sides; if one is positive and the other is negative then they are perpendicular. Signup and view all the answers

Study Notes

Interior Angles of Polygons

Formula for sum of one interior angle: ((n-2)180/n).
To find the number of sides (n) of a polygon, set the sum of interior angles equal to ((n-2)180).

Parallelogram and its Properties

A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel.
To find the intersection point in a parallelogram, apply the midpoint formula to the coordinates of a diagonal.

Midpoint and Slope Formulas

Midpoint formula: ((x₁+x₂)/2, (y₁+y₂)/2).
Slope formula: (m = (y₂-y₁)/(x₂-x₁)).

Finding Points and Sides

To find coordinates of an unknown point in a figure, calculate the slope between known points and apply it to other coordinates.

Identifying Quadrilaterals

Use the Distance Formula to prove congruency of sides and the Slope Formula to confirm parallel lines when identifying parallelograms.
Distance formula: (d = \sqrt{(x₂ - x₁)² + (y₂ - y₁)²}).

Types of Quadrilaterals

Rhombus: A parallelogram with four congruent sides.
Rectangle: A quadrilateral with four right angles.
Square: A parallelogram that combines properties of both rhombus and rectangle.

Characteristics of Special Quadrilaterals

Rhombus: Diagonals are perpendicular and bisect a pair of opposite angles.
Rectangle: Diagonals are congruent.
Square: Diagonals are both perpendicular and congruent.

Trapezoids

A trapezoid has one pair of parallel sides.
Base angles: Two consecutive angles sharing a base.
Legs: Non-parallel sides of a trapezoid.

Identifying Trapezoids

Check slopes of opposite sides to determine parallelism.
Prove legs are congruent using the Distance Formula to identify isosceles trapezoids.

Trapezoid Mid Segment

The midsegment of a trapezoid is calculated as (1/2(b₁ + b₂)).

Kites

A kite has two pairs of consecutive congruent sides with no pairs of opposite sides being congruent.
Characteristics include one pair of opposite angles being congruent and perpendicular diagonals.

Finding Rectangles on a Coordinate Plane

To identify a rectangle, verify the slopes of pairs of opposite sides; they must be negative reciprocals indicating perpendicularity.

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Description

This quiz covers essential concepts related to the interior angles of polygons, properties of parallelograms, and formulas for midpoints and slopes. You'll explore how to identify different types of quadrilaterals using distance and slope formulas. Test your knowledge on these geometric principles!