Bisecting and Trisecting Segments
Bisection and trisection involve cutting something into two or three equal parts. If you’re a fan of bicycles and tricycles and bifocals and trifocals — not to mention the biathlon and the triathlon, bifurcation [more…]
Bisecting and Trisecting Angles
The terms angle bisection and angle trisection describe two ways in which you can divide up an angle equally into two (or three) smaller, congruent angles. Their definitions are often used in proofs. [more…]
Geometry Formulas You Should Know
Below are several of the most important geometry formulas, theorems, properties, and so on that you use for solving various problems. If you get stumped while working on a problem and can’t come up with [more…]
How to Solve a Common-Tangent Problem
The common-tangent problem is named for the single tangent segment that’s tangent to two circles. Your goal is to find the length of the tangent. These problems are a bit involved, but they should cause [more…]
How to Solve Similar Triangle Problems with the Side-Splitter Theorem
You can solve certain similar triangle problems using the Side-Splitter Theorem. This theorem states that if a line is parallel to a side of a triangle and it intersects the other two sides, it divides [more…]
Using the Hypotenuse-Leg-Right Angle Method to Prove Triangles Congruent
The HLR (Hypotenuse-Leg-Right angle) theorem — often called the HL theorem — states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle [more…]
How to Do an Indirect Proof
Indirect proofs are sort of a weird uncle of regular proofs. With an indirect proof, instead of proving that something must be true, you prove it indirectly [more…]
Definitions and Theorems of Parallel Lines
Parallel lines are important when you study quadrilaterals because six of the seven types of quadrilaterals (all of them except the kite) contain parallel lines. The eight angles formed by parallel lines [more…]
Working with More than One Transversal
When a parallel-lines-with-transversal drawing contains more than three lines, identifying congruent and supplementary angles can be kind of challenging. The following figure shows you two parallel lines [more…]
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…]
