| A | B |
|---|
| A net is a 3 dimensional figure____ | that unfolds to a flat surface |
| Probablility = | the number possible divided by total |
| Arc Length = | (angle/360)πd |
| Area of a sector= | (angle/360)(πrˆ2) |
| 45-45-90 leg to hypotenuse | Multiply by the square root of 2 |
| 30-60-90 short to long | multiply by the square root of 3 |
| An exterior angle of a triangle = sum of | the 2 remote interior angles |
| opposite angles of a parallelogram are | congruent |
| Vertical angles are | congruent |
| An octagon has | 8 sides |
| A heptagon has | 7 sides |
| The converse is created by | changing the order |
| A radius drawn to a tangent of the circle | is perpendicular to the tangent line. |
| Perpendicular lines have slope | opposite reciprocals |
| Parallel lines have the _____ slope | same |
| Midpoint formula | (add x's/2, add y's/2) |
| Possible measures of the third side of a triangle are found by | between adding the two sides and subtracting the two sides |
| Across from the smalles angle is the | smallest side |
| A radius perpendicular to a chord | bisects chord and its arc |
| A segment drawn parallel to a side of a triangle, divides the other 2 sides | proportionally |
| Formula for a median of a triangle (mid segment) | 1/2 the base |
| 2 angles whose sum is 90 | complementary |
| The sum of the angles of a quadrilateral | 360 |
| State 3 properties of a rhombus | 4 congruent sides, diagonals are perpendicular, diangonal bisect the angles, opposite sides and angles are congruent |
| State 3 properties of a rectangle | 4 congruent 90 degree angles, diagonals are congruent, diagonals bisect each other, opposite sides and angles are congruent |
| opposite angles of a quadrilateral inscribed in a circle | are supplementary |
| Stgate 3 properties of a square | 4 congruent angles, 4 congruent sides, diagonals are congruent and perpendicular |
| Corresponding angles | same side of the transversal, one is exterior, one interior, non-adjacent |
| Alternate interior angles | 2 non-adjacent, interior angles on opposite sides of the transversal |
| Consecutive interior angles (same side interior) | 2 interior angles on the same side of the transversal, if lines are parallel they are supplementary |
| 2 ways to prove triangles similar | AA~ and SAS ~ |
| Similar | same shape, different size |
| Similar triangles have ____ angles and _____ sides | congruent, proportional |
| An angle of elevation | opens from the horizontal upwards |
| An angle of depression | opens from the horizontal downwards |
| <a,b>+<c,d>= | <a+c, b+d> |
| An angle bisector divides the angle | into two congruent angles |
| A decagon has | 10 sides |
| The inverse is created by | inserting nots or taking out a not |
| The contrapositive is created by | changing the order and inserting the nots |
| The sum of the angles in a triangle is | 180 |
| Consecutive angles of a parallelogram are | supplementary (180) |
| The sum of the exterior angles, one at each vertex, of a polygon is | 360 |
| In a polygon, an exterior and an interior angle | are supplementary |
| Diagonals of a rectangle are | congruent |
| Diagonals of a parallelogram | bisect each other |
| 2 angles whose sum is 180 | are supplementary |
| State the Pythagorean Theorem | aˆ2 +bˆ2=cˆ2 |
| Use the Pythagorean Theorem when | you know two sides looking for the 3rd side |
| The perimeter is found by | adding all the sides |
| State the distance formula | the square root of (subtract the x's and square it PLUS subtract the y's and square it ) |
| Name 5 ways to prove triangles congruent | SAS, SSS, ASA, AAS, HL |
| Name two ways that triangles cannot be proved congruent | AAA and SSA |
| The geometric mean places the | x in the mean positions 2/x=x/6 |
| The central angle of a circle = | its arc |
| The inscribed angle of a circle = | 1/2 arc |
| An interior angle of a circle = | 1/2 SUM of the intercepted arcs |
| An exterior angle of a circle= | 1/2 DIFFERENCE (subt) of its intercepted arcs |
| A party hat on a circle (angles) | exterior angle and the minor arc are supplementary |
| Sin x= | opposite/hypotenuse |
| cos x= | adjacent/hypotenuse |
| tan x= | opposite/adjacent |
| On a calculator, when you find the ____ you must use the _____key | angle, shift |
| Formula for the area of a regular polygon | 1/2 ap (apothem, perimeter) |
| Area of a trapezoid | 1/2(b+b)h |
| Tessellation is the covering of a plane with | non-overlapping, non-gapping polygons |
| A reflection is | flipping the figure over a line (mirror image) |
| A rotation is | moving the object through an angle (turning it) |
| A translation is | a slide in any direction |
| A dilation is | enlarging or shrinking an object |
| An altitude | is drawn from the vertex perpendicular to the opposite side |
| A median | is drawn from the vertex to the midpoint of the opposite side |
| A perpendicular bisector | a line drawn perpendicular to the side of a triangle |
| radius= | 1/2 diameter |
| Equation of a circle | (x-h)ˆ2+(y-k)ˆ2=rˆ2 (h,k) center r is the radius |
| Angles of parallel lines | obtuse<=obtuse< acute <=acute < obtuse<+acute<=180 |
| Constructions | From the point make two arcs onto the figure. From these arcs you just made, "fish". Draw the line. |
| The acute angles of a right triangle | are complementary |
| Syllogism's conclusion | if of the first sentence, then of the last sentence |
| Logic symbols | ~ means not, ^ means and |
| A trapezoid's diagonals | divides the trapezoid into 2 similar triangles found on top and on the bottom. The sides of these two triangles are proportional |
| Across from the smallest angle of a triangle is | the smalles side of the triangle. |
| Across from the longest side of a triangle is | the largest angle of the triangle. |
| The ratio (scale factor) of 2 similar polygons is found by | finding a pair of corresponding sides and making a fraction. Reduce. |
| If you know 3 lengths and need to determine if it is a triangle | small side + medium side must be larger than the biggest side. |
| In a right triangle, a segment drawn perpendicular to the hypotenuse sets up the following proportion (altitude rule) | Part of hypotenuse: altitude=altitude:other part of the hypotenuse |
| In a right triangle, a segment drawn perpendicular to the hypotenuse sets up the following proportion (leg rule) | part of the hypotenuse closest to leg: leg=leg: whole length of the hypotenuse |
| A triangle inscribed in a semicircle is | a right triangle. |
| To find coordinates of the top right vertex of a parallelogram placed at the origin, | add the x's and the y's of the other vertices. |
| A trapezoid's diagonals will | never bisect each other. |
| Exterior angles of a regular polygon | sum is 360 (Note: 360 is always a division problem) |
| Two chords that intersect in a circle | the product of the parts of one chord=the product of the parts of the other chord. ab=cd |
| An angle whose vertex is outside a circle that passes through the circle or is tangent to the circle | outer length times whole length = outer length of the other side times the whole length |
| The sides of a "party"hat on a circle are | congruent. |
| When measuring stories of a building, remember to | add each height of the stories together (do not measure the roofs!!!) Then multiply by the scale number. |
| Due south or Due north problems | subtract from 90. |
| To find the diameter's length given 2 end points | Use the distance formula. |
| To find the radius given the center point and a point on the circle, | use the distance formula. |
| Point symmetry | turning the figure upside down and it looks exactly the same. |
| Find the the slope in a right triangle figure. | Rise/Run Vertical number/horizontal number. If going up (left to right) then a positive answer. If down a negative answer. |
| A plane is determined by | 3 non-collinear points. (don't forget the non) |
| Two points determine | a line. |
| Base angles of an isosceles triangle | are congruent. |
| A star is inscribed in a circle. To find the length of an arc from one tip to the next tip | take 360 and divide it by how many tips around the whole circle. |
| Joining the midpoints of a quadrilateral results in a | parallelogram. |
| A sphere inscribed in a cube takes up about | half the volume of the cube. |
| Central angle of a regular polygon | 360 divided by number of sides. (same as exterior angle) |
| A quadrilateral inscribed in a circle has opposite angles | supplementary. (draw - one angle is obtuse and the other acute - therefore supplementary.) |
| The slope of a line | subtract the y's / subtract the x's |
