Cheatography

# Geometry Finals (Semester 2) Cheat Sheet by frog.lover28

geometry finals (semester 2) study guide :)

### chapter 6 - relating lines to planes

 VOCAB plane - a surface such that if any two points on the surface are connected by a line, all points of the line are also on the surface. noncop­lanar - not on the same plane. coplanar - on the same plane. foot - point of inters­ection of a line and a plane. POSTULATES Three noncol­linear points determine a plane. If a line intersects a plane not containing it, then the inters­ection is exactly one point. If two planes intersect, their inters­ection is exactly one line. THEOREMS A line and a point not on the line determine a plane. Two inters­ecting lines determine a plane. Two parallel lines determine a plane. If a line is perpen­dicular to 2 distinct lines that lie on a plane and that pass through its foot, then it is perpen­dicular to the plane. If a plane intersects 2 parallel planes, the lines of inters­ection are parallel.

### chapter 8 - ratio and proportion

 THEOREMS Means-­Ext­remes Products Theorem - a/b = c/d -> ad=bc Means-­Ext­remes Ratio Theorem - pq=rs -> p/r=s/q etc. Arithmetic mean example: given 3 & 7, 3+27/2= 15 Geometric mean example: given 3 & 7, 3/x = x/27 x=+ or - 9 AAA (angles) - similar AA (angles) - similar Side-S­plitter Theorem - ab/bc = ae/ed TERMS Dilati­on/­Red­uction Similarity - same shape but not size

### chapter 10 - circles

 TERMS concentric circle - same center with different size chord - points connected by a segment on a circle diamet­er/­radius secant­s/t­angents THEOREMS If a radius is perpen­dicular to a chord then it bisects it (reversed too). The perpen­dicular bisector of a chord passes through the center of a circle. If 2 chords are equidi­stant from the center then they are congruent (reversed too). secant­/ta­ngent theorems - example: 1/2 (large angle - medium angle) = small angle chords: ev . en = el . se tp (tangent) squared = (pr)(pq aka external part of secant) pb . pa (external part of secant) = pd . pc (external part of secant)

### chapter 12

 TERMS bases lateral faces lateral edges slant height altitude (height) LA: Lateral surface area - no bases TA: Total surface area - with bases volume

### chapter 7 - triangle applic­ation theorems

 THEOREMS The sum of the measures of the 3 angles of a triangle is 180. The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. A segment joining the midpoints of 2 sides of a triangle is parallel to the third side, and its length is one-half the length of the third side (midline theorem). No choice theorem - if 2 angles of a triangle are congruent then the remaining ones are also. AAS - angle angle side FORMULAS sum of angles in polygon = (sides - 2)180 exterior angles = 360 diagonals = sides(­sides - 3)/2 exterior angle = 360/sides

### chapter 9 - a lot of different things

 RADICAL REVIEW squared root of 48 = 4 radical 3 squared root of 5/3 = squared root of 15/3 CIRCLES circum­ference - pi d area - pi r squared sector - fraction of circle area arc - fraction of circum­ference secants - through circle tangent - edge of circle (exter­nal­/in­ternal) RIGHT TRIANGLE ALTITUDES h squared = x . y a squared = x . c b squared = y . c OTHER pythag­orean theorem - a squared + b squared = c squared distance formula - squared root (x2 - x1) squared + (y2 - y1) squared 30 60 90 45 45 90 SOH CAH TOA

### chapter 11 - area

 I don't feel like writing all of the area formulas but here are the ones you need to know... square­/re­ctanle triangle parall­elogram trapezoid (and median) kite polygons circle, sectors, segments hero formula: squared root of s(s-a)­(s-­b)(s-c)