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geometry finals (semester 2) study guide :)
chapter 6 - relating lines to planesVOCAB | 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 proportionTHEOREMS | 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 - circlesTERMS | 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 12TERMS | 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 theoremsTHEOREMS | 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 thingsRADICAL 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 - areaI 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) |
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