Cassie Greco Math Midterm Review Conjunctions- combine 2 sentences using the word and. Symbol= ^ (looks like an upside down v) Disjunctions- combine 2 sentences using the word or. Symbol = v (what looks like a v) Conditionals- combine 2 sentences using the words if.then. The two parts to this are the hypothesis and conclusion. Hypothesis comes after the word if. Conclusion comes after the word than. Symbol= (arrow to the right) Biconditionals- combines 2 sentences using the words if and only if. Symbol= (arrow pointing right and left) Inverse- negating hypothesis and conclusion. Symbol= ~ Converse- switching hypothesis and conclusion. Contrapositive- doing the inverse and converse to the conditional. Logically equivalent- same truth-value. Conditional and contrapositive. Inverse and converse. Conjunction Truths: T ^ T- T T ^ F- F F ^T- F F ^ F- F

Disjunction Truths: T vT- T T v F- T F v T- T F v F- F

Conditional Truths: T ---> T- T T ---> F- F F --->T- T F ---> F- T Biconditional Truths: T < --- > T- T T F F

< ---> F- F < ---> T- F < ---> F- T

Truth Table Example: (p v q) ---> q P T T F F Q T F T F PvQ T T T F (p v q) ---> q T F T T

**Highlighted boxes= how you always start a truth table** Angle- 2 rays same end point. Symbol= < Right Angle- 90. Acute- less than 90. Obtuse- greater than 90 less than 180. Straight- 180. Complementary- sum equals 90.

Supplementary- sum equals 180. Vertical- angles across from each other. They are congruent. Congruent- equal to. Symbol = Adjacent- next to. Bisector- cuts segment at midpoint into congruent parts. Angle bisector- divides angle into congruent parts. Midpoint- makes 2 congruent parts. Parallel- lines that dont intersect. Perpendicular lines- form right angles. Reflexive- equal to each other. Alternate interior, exterior, and corresponding angles.

Polygon- closed figure with 3 or more sides. 3-triangle 4-quadrilateral 5-pentagon 6-hexagon 7-septagon/neptagon 8-octagon 9-nonagon 10-decigon Sum of exterior angles of a polygon is always 360. To find the exterior angles of a polygon divide 360 with the number of sides. To find interior angles in a polygon use: 180 (n-2) n- number of sides Adding one interior and one exterior angle will give you 180. To find each angle use: 180 (n-2) 2 When you get two vertical angles set them equal to each other. Central angle of circle- vertex is the center. Measure of central angle is equal to the intercepted arc. Inscribed Angle- vertex is on the circle. Measure of this angle is half the intercepted arc. Or the arch is twice the angle. Formed by cords- they dont pass through center. Angle equals: sum of intercepted arc 2

Tangent:

Secant:

Both:

Angle major minor 2 Measures of chords: (AE)(EB)=(CE)(ED)

A Both: (AF)2= (AB)(AC) F B

C

Measure of Secant: (AB)(AC)=(AD)(AE) A

D

B

E

C

Reflex over the x axis: (x,y)- (x, -y) Reflex over the y axis: (x,y)- (-x,y) y=x becomes x=y glide reflection- translation followed by reflection or reflection followed by translation. dilation- multiplies each number by the number given. example: D2 (1,1)- (2,2) Rotation90= 1 quadrant R90 (x,y) (-y,x) 180= 2 quadrants R180 (x,y) (-x, -y) 270= 3 quadrants R270 (x,y) (y, -x) Orientation- clockwise or counter clockwise Isometry- distance Composition of transformation- symbol : o do anything after the o first and anything before the o second. example: T (2,1) o D2 to solve do D2 first than T(2,1) When it says Ro that mean rotate 180. Dilation- no isometry.

Direct isometry- preserves distance and orientation. Opposite isometry- preserves distance and orientation changes. Proving Lines are Parallel. 1. A pair of alternate interior angles are congruent (most common hint look for the z.)

2. A pair of corresponding angles are congruent (hint look for the f.)

3. A pair of interior angles on the same side of the transversal are supplementary.

4. Both lines are perpendicular to the same line (least common.) Proving Parallelograms. 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite sides are parallel. 3. One pair of opposite sides are parallel and congruent. 4. Both pairs of opposite angles are congruent. 5. Prove the diagonals bisect each other. Rectangles- have all properties of a parallelogram. It has 4 right angles. diagonals are congruent. Rhombus- all properties of a parallelogram. All sides are congruent. Diagonals are perpendicular to each other, and they bisect each other. Square- prove 4 right angles and 4 congruent sides. Distance 4 times slope 4 times.

Midpoint-

Distance formula-

Slope formula-

Types of slopes:

Parallel slopes- lines are parallel when their slopes are the same. example: y=3x + 2 m=3 y=3x 1 m=3

Perpendicular slopes- they are perpendicular when their slopes are negative reciprocals of eachother. example: y=2x + 2 m= 2 y= -1/2 x m= -1/2 When to have the same slope it is a parallelogram. Proving right triangles- show 2 sides are perpendicular. Use slope formula. NEGATIVE RECIPROCIALS. Proving isosceles triangles- show 2 sides are congruent. Use distance formula. 2 CONGRUENT SIDES. Proving Trapezoid- Prove one pair parallel and one pair not. Use slope formula. 2 CONGRUENT 2 NOT. if isosceles- proves 2 non-parallel sides congruent. Distance formula. 2 CONGRUENT SIDES. Standard form of an equation: y= mx + b m= slope b= y intercept Equation of a circle(x-h)2 + (y-k) 2= r2

h=center r=radius. (negative becomes positive!!) Locus- set of points that satisfy a given condition. 5 theorems. 1. A locus of points equidistant from 2 fixed points is a line down the middle. 2. A locus of points to 2 intersecting lines are 2 bisecting lines. (hint make a t or an x) 3. The locus of points equidistant from 2 parallel lines is one parallel line down the middle. 4. A locus of points equidistant from a parallel line is 2 parallel lines (hint: above & below.) 5. A locus of points from a fixed point is a circle. Volume of a cube: v= e3 e= edge s= side Volume of a rectangle: v= lwh Volume of a cylinder (given) v=Bh B= area of base h= height or altitude v= r2 h

Lateral Area of cylinder (given) l= 2 rh Surface area of cylinder s= 2rh + 2r2 Volume of a sphere (given) v= r3 Surface area of a sphere (given) sa= 4 r2. Volume of a pyramid (given) B= area of base Surface area of pyramid: L+B Lateral Area of Pyramid: 4(area of the side) Height= center to top slant height= top to middle of bottom Prism: v= Bh Proportions with similar triangles: shortest side on one triangle will correspond with the shortest side of the other. Similar triangle proofs: prove all with the AA theorem (angle, angle) Random Vocabulary/ Things to know: concurrence- 3 or more lines connecting at a point

centroid- 3 medians intersection. Divides in a 2:1 ratio. altitudes- segment from any vertex perpendicular to opposite side. orthocenter- 3 altitudes intersection. incenter- 3 angles bisector intersection. circumcenter- perpendicular bisectors Pythagorean theorem: a2+b2=c2 tentahedron- 4 faces cube- 6 faces octahedron- 6 faces docdecahedron- 12 faces icosahedron- 20 faces scalene- no congruent sides isosceles- 2 congruent sides equilateral- 3 congruent sides acute- all acute angles right- 1 right angle obtuse- one obtuse angle equiangular- 3 congruent angles sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side. longest side of a triangle is opposite the largest angle. exterior angle of a triangle is greater than either of the 2 non adjacent interior angles.

glide reflection- composition of reflection and a translation. isometry- keeps length. orientation- label order