Geometry

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Identifying the Seven Quadrilaterals

A quadrilateral is a polygon with four sides. There are seven quadrilaterals, some that are surely familiar to you, and some that may not be so familiar. Check out the following definitions and the quadrilateral [more…]

How Various Quadrilaterals Are Related

The quadrilateral family tree in the figure below shows you the relationships among the various quadrilaterals. The following list of questions gives you a taste of some of these relationships. [more…]

How to Calculate the Area of a Regular Polygon

A regular polygon is equilateral (it has equal sides) and equiangular (it has equal angles). To find the area of a regular polygon, you use an apothem — a segment that joins the polygon’s center to the [more…]

How to Calculate the Area of a Regular Hexagon

One way to find the area of a regular hexagon is by first dividing it into equilateral triangles. You also need to use an apothem — a segment that joins a regular polygon’s center to the midpoint of any [more…]

Using Two Equidistant Points to Determine a Perpendicular Bisector

You can use two equidistant points to determine the perpendicular bisector of a segment. (To “determine” something means to fix or lock in its position, basically to show you where something is.) Here’s [more…]

Using a Point on a Perpendicular Bisector to Prove two Segments Congruent

You can use a point on a perpendicular bisector to prove that two segments are congruent. If the point is on the perpendicular bisector of a segment, then it’s equidistant from the endpoints of the segment [more…]

How to Determine the Area of Sectors and Segments of a Circle

Mark off a section of a circle with an arc and a chord, and you have a segment (this type of segment has nothing to do with a line segment). Throw a couple of radii around an arc, and you have a sector [more…]

How to Determine the Measure of an Angle whose Vertex Is on a Circle

Of the three places an angle’s vertex can be in relation to a circle (inside, on, or outside the circle), the two types of angles that have their vertex [more…]

How to Determine the Measure of an Angle whose Vertex Is Outside a Circle

An angle that intersects a circle can have its vertex inside, on, or outside the circle. This article discusses the three types of angles that have their vertex outside a circle: secant-secant angles, [more…]

How to Use the Chord-Chord Power Theorem

The Chord-Chord Power Theorem was named for the fact that it uses a chord and — can you guess? — another chord!

Chord-Chord Power Theorem: If two chords of a circle intersect, then the product of the measures [more…]

How to Use the Tangent-Secant Power Theorem

You can solve some circle problems using the Tangent-Secant Power Theorem. This theorem states that if a tangent and a secant are drawn from an external point to a circle, then the square of the measure [more…]

How to Use the Secant-Secant Power Theorem

You can use the Secant-Secant Power Theorem to solve some circle problems. This theorem involves — are you sitting down — two secants! (If you’re trying to come up with a creative name for your child like [more…]

How to Use the Golden Ratio

The golden ratio is a famous geometry idea with a connection to ancient Greece. (When it came to mathematics, physics, astronomy, philosophy, drama, and the like, those ancient Greeks sure did kick some [more…]

Applying the Transversal Theorems

When you cross two lines with a third line, the third line is called a transversal. You can use the transversal theorems to prove that angles are congruent or supplementary. [more…]

Using Auxiliary Lines in Proofs

The following proof introduces you to a new idea: adding a line or segment (called an auxiliary line) to a proof diagram to help you do the proof. Some proofs are impossible to solve until you add a line [more…]

Using the Angle-Angle-Side Method to Prove Triangles Congruent

The AAS (Angle-Angle-Side) theorem states that if two angles and a nonincluded side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. The following [more…]

The Geometry of Projectile's Motion

Projectile motion is the motion of a “thrown” object (baseball, bullet, or whatever) as it travels upward and outward and then is pulled back down by gravity. The study of projectile motion has been important [more…]

Properties of Parallelograms

The properties of the parallelogram are simply those things that are true about it. These properties concern its sides, angles, and diagonals.

The parallelogram has the following properties: [more…]

How to Determine the Earth's Circumference

You can figure out the earth's circumference using a geometric formula that's over 2,000 years old! Contrary to popular belief, Christopher Columbus did not discover that the Earth is round. Eratosthenes [more…]

How to Determine the Distance to the Horizon

Even before Columbus sailed across the Atlantic Ocean (thus “proving” the Earth was round), mathematicians had already developed a very simple formula to calculate the distance to the horizon. Although [more…]

Applying the Pythagorean Theorem

The Pythagorean Theorem has been known for at least 2,500 years. You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the [more…]

Cabri Jr. versus GeoMaster on the TI-84 Plus Calculator

Because the TI-84 Plus comes equipped with two geometry applications, Cabri Jr. and GeoMaster, you can now do your geometric investigations on the calculator. Granted, the calculator screen is rather small [more…]

Quit GeoMaster on the TI-84 Plus Calculator

You can use either a clean way or a dirty way of quitting the GeoMaster application on the TI-84 Plus calculator. The clean way truly terminates GeoMaster, [more…]

Construct Points for Geometric Figures with the TI-84 Plus

You can tell the TI-84 Plus calculator where you want to construct a freestanding point in two ways: Use the arrow keys to identify the location of the point, or tell the calculator the coordinates of [more…]

How to Construct Perpendicular Bisectors with GeoMaster

In GeoMaster on the TI-84 Plus graphing calculator, a perpendicular bisector can be constructed to an already existing line, segment, ray, vector, or side of a polygon or triangle. To construct a perpendicular [more…]

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