Geometry for College Students

Let P,Q, and R be the points of tangency of the incircle of ∆ABC with sides BC, CA, and AB, respectively. Then lines AP, BQ, and CR: are concurrent. Gergonne point Point of congruency of lines AP, BQ, and CR, where P,Q, and R are the points of tangency of the incircle of ∆ABC. Ceva’s […]

Pre College Math Chapter 6 Geometry Formulas

Formula for a Parallogram A=b×h Formula for a Triangle A=½×b×h Formula for a Trapezoid A= a+b/2×h or A=½×h×(a+b) Formula for Circles when finding the diameter D=2×R Formula for Circles when finding the radius R=d/2 Formula for finding the circumference when you have the diameter C=3.14×D Formula for finding the circumference when you have the radius […]

Geometry Regents Review

Collinear Points points that lie on the same line complementary angles have a sum of 90 degrees supplementary angles have a sum of 180 degrees exterior angle theorem in a triangle; two interior angles equal the opposite exterior angle (x+y=z) centroid in a triangle; intersection of medians, (2x+x=3x) orthocenter in a triangle; intersection of altitudes […]

Pearson Texas Geometry: Topic 1 Tools of Geometry Goodrich ISD, TX

Straight angle Angle whose measure is 180°. Obtuse angle Angle whose measure is between 90° and 180°. Angle Is formed by two rays with the same endpoint. Congruent angles Angles with the same measure. Measure of an angle Absolute value of the difference of the real numbers paired with the sides of the angle Right […]

Geometry Constructions

Perpendicular bisector construction Perpendicular line through a point Copy an angle Construct an angle bisector. Parallel line through a point construction make a perpendicular line through the point then make a perpendicular line through the new line. Use patty paper Copying a Segment median construction Find the midpoint of one side then connect the opposite […]

Geometry Patty Paper Conjectures

Altitudes of a Triangle If you have the altitudes of a triangle, then they will intersect at the orthocenter. Triangle Midsegments If you have the midsegment of a triangle, then it will be half the length of the corresponding base. Triangle midsegments If you have a midsegment, then it is parallel to the corresponding base. […]

Geometry A – Nets and Drawings for Visualizing Geometry

Which three-dimensional figure matches the next below? (it looks like a sideways T made out of squares) B (its a cube) A piece of paper is cut and then folded into the rectangular prism as shown below. Which side is the bottom, and which side is on the left of the rectangular prism? B is […]

Polyatomic Ions, Geometries, and Nomenclature

Ammonium NH4+ Acetate C2H3O2– Carbonate CO32- Cyanide CN– Hydroxide OH– Nitrate NO3– Nitrite NO2– Sulfate SO42- Sulfite SO32- Phosphite PO33- Phosphate PO43- Perchlorate ClO4– Chlorate ClO3– Permanganate MnO4– Hydrogen Carbonate (Bicarbonate) HCO3– Dichromate Cr2O72- Electron: Linear Molecular: Linear Electron Groups: 2 Bonding Groups: 2 Lone Pairs: 0 Electron: Trigonal Planar Molecular: Trigonal Planar Electron Groups: […]

Molecular Geometry and Bond Theories

bond angles the angles made by the lines joining the nuclei of the atoms in a molecule VSEPR model a model that accounts for the geometric arrangements of shared and unshared electron pairs around a central atom in terms of the repulsions between electron pairs electron domains in the VSEPR model, a region about a […]

Molecular Geometry Test Questions

Lone Pairs: 0 Bonding Groups: 2   Molecular Geometry? Bond Angle/s? Molecular Geometry LINEAR   180 degrees Lone Pairs: 0 Bonding Groups: 3   Molecular Geometry? Bond angle/s? Molecular Geometry TRIGONAL PLANAR   120 degrees Lone Pairs: 0 Bonding Groups: 2     Electron Pair Geometry Electron Pair Geometry LINEAR Lone Pairs: 0 Bonding Groups: […]

2 bonding pairs, 0 lone pairs electron geometry: linear molecular geometry: linear bond angle: 180o       3 bonding pairs, 0 lone pairs    electron geometry: trigonal planar molecular geometry: trigonal planar bond angle: 120o    2 bonding pairs, 1 lone pair   electron geometry: trigonal planar molecular geometry: bent bond angle: about 118o […]

Molecular Geometry/Hybridizati

Linear 2 electron pairssp hybridization0 lone pairs Trigonal Planar 3 electron pairssp2 hybridization0 lone pairs Bent (A) 3 electron pairssp2 hybridization1 lone pair Tetrahedral 4 electron pairssp3 hybridization0 lone pairs Trigonal Pyramidal 4 electron pairssp3 hybridization1 lone pair Bent (B) 4 electron pairssp3 hybridization2 lone pairs Trigonal bipyramidal 5 electron pairsdsp3 hybridization0 lone pairs Seesaw […]

Electron Pair and Molecular geometry

2 electron pairs (EPG) Linear Linear Bond Angle 180 degrees 3 electron pairs (EPG) trigonal planar trigonal planar bond angle 120 degrees 4 electron pairs (EPG) Tetrahedral Tetrahedral Bond angle 109.5 degrees 5 electron pairs (EPG) Trigonal bipyramidal Trigonal bipyramidal bond angle 120 and 90 degrees 6 electron pairs (EPG) Octahedral Octahedral bond angle 90 […]

Geometry A – Nets and Drawings for Visualizing Geometry

question Which three-dimensional figure matches the next below? (it looks like a sideways T made out of squares) answer B (its a cube) question A piece of paper is cut and then folded into the rectangular prism as shown below. Which side is the bottom, and which side is on the left of the rectangular […]

Geometry – Flashcard

question A geometric figure created without using tools is an answer sketch question 2 or more lines that are not in the same plane answer skew lines question location in space answer point question points where a line segment begins and ends answer endpoints question straight continuous arrangement of an infinite number of points answer […]

geometry exam study guide

question Point answer A location question Does a point have length? answer NO question Does a point have width? answer NO question Does a point have thickness? answer NO question Line answer An infinite set of points that extends in two directions question Does a line have length? answer yes question Does a line have […]

Geometry – Flashcard

Question Answer Opposite Ray Two rays that point in opposite directions Congruent Angles No measurements Line Stretches in 2 directions forever Obtuse Angle Larger than 90A° less than 180A° Ray A portion of a line with only one endpoint Congruent segment Same size and shape Angle bisector Divide an angle into 2 congruent angles Acute […]

Geometry Proofs

Question Answer A=A Reflexive Property Figures that lie on the same line Colinear If A=B then B=A Symmetric Property If not hypothesis, if not P, then not conclusion not Q Inverse Small basic set of agreed on assumptions and premises on entire structure of logic is devised Axiomatic System If A=B and C=D the A-C […]

Geometry Semester 2 Final Study Guide

question Parallelogram answer A quadrilateral in which both pairs of opposite sides are parallelogram. question Rhombus answer A parallelogram which has four congruent sides. question Rectangle answer A parallelogram which has four right angles. question Square answer A parallelogram which has four congruent sides and four right angles. question Kite answer A quadrilateral with two […]

Geometry quiz 4

Select the postulate about two planes. Postulate 5: If two planes intersect, then their intersection is a line. Select the postulate that states a line is determined by two points. Postulate 2: Through any two different points, exactly one line exists. Select the postulate that specifies the minimum number of points in space. Postulate 1b: […]