honors geo review units 5 and 6

Similar Polygons

Similar Polygons

two polygons whose corresponding angles are congruent and whose corresponding sides are proportional

Triangle Similarity

AA, SSS, SAS

Law of Cosines

a²=b²+c²-2bcCosA

Law of Sines

sinA/a = sinB/b = sinC/c

Angle-Bisector Theorem

If a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.

Center-Radius Form

(x-h)²+(y-k)²=r²

How Do You Complete the Square?

Add (b/2)^2 to both sides of the equation

What is a line tangent to the circle?

It intersects the circle only once and is always perpendicular to a radius drawn to the intersection point

What is a chord of a circle?

A chord is a line segment joining two points on a circle.

Chord Theorum

A radius is perpendicular to a chord of a circle if it bisects the chord

Tangent theorum

If two tangent segments share a common endpoint outside of a circle, then they are congruent

Measure of an arc is equal to

Measure of its central angle (the angle that is formed by connecting the radius to both ends of the arc)

Inscribed Angle Theorum

If an angle is an inscribed angle, then it has a measure equal to one half the measure of its intercepted arc

Circumference

2πR

Area of a Circle

πR²

Arc Length

(x/360)2πR or (x/2π)2πR

Sector Area

(x/360)πR² or (x/2π)πR²

Side Splitter Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.