Geometry Concepts for review

G.1 a,b,c  LOGIC

Students use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include:

a) identifying the converse, inverse, and contrapositive of a conditional statement

b) translating a short verbal argument into symbolic form

c) determining the validity of a logical argument

Please review this material with the following material:
.  Use chain reasoning to make a logical conclusion given a set of statements.

Section 2.2 Reasoning and Direct Proofs

p. 70 Inductive Reasoning,

p. 71 Counterexample,

p. 72 Deductive Reasoning

Please work these examples and check them against my key which you may request- feel free to work together - using social distancing of course!

Remember you may access the video section of the book to reinforce your knowledge

Try this to test your logic skills IXL

I'm looking forward to hearing from you!!

Unit 2 Coordinate Geometry, Basic Constructions and Equations of Circles

G.3 solve problems involving symmetry and transformations. This will include:

a) investigating and using formulas for determining distance, midpoint, and slope

b) applying slope to verify and determine whether lines are parallel or perpendicular

G.4 construct and justify the construction of
a) line segment congruent to a given line segment
b) the perpendicular bisector of a line segment
e) the bisector of a given angle
f) an angle congruent to a given angle

G.12 solve problems involving equations of circles.

Midpoint and Distance:
Big Ideas Geometry 1.3 #15-37

Constructions

More constructions

You will need to have your own compass and paper /or go to Desmos/geometry and practice online

Equations of a circle:

Unit 3 Angle relationships with Intersecting and Parallel lines

G.2 Use the relationships between angles formed by two lines intersected by a transversal to:

a) prove two or more lines are parallel

b) solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal

G.4 construct and justify constructions of:

c) a perpendicular to a given line from a point not on the line

d) a perpendicular to a given line at a given point on the line

g) a line parallel to a given line through a point not on the line

Fun Practice - work your way through the 10 problems

Constructions - the above link includes the perpendicular

More practice on parallel lines

Proofs on parallel lines

Chapter Review pg. 149-151 #1-26

Unit 4 Circles G.11a, b

G.11 solve problems, including practical problems, by applying properties of circles. This will include determining:

a) angle measures formed by intersecting chords, secants, and/or tangents

b) lengths of segments formed by intersecting chords, secants, and/or tangents;

Video on Linear relationships in circles
Practice pg 493-493#1-26

Video on Central and Inscribed Angles
Practice pg. 500#1-24

Video on Tangents
Practice pg. 508#3-29

There are videos in your text and there are more of Mr. Harrington's videos if you come across a concept you have forgotten.

Chapter review Pg 523#1-48  This includes equations of circles too

Unit 5  G.5abcd Triangle relationships

G.5 given information concerning the lengths of the sides and/or measures of angles in triangles, solve problems, including practical problems. Including:

a) ordering the sides by length, given angle measures

b) ordering the angles by degree measure, given side lengths

c) determining whether a triangle exists

d) determining the range in which the length of the third side must lie

Triangle Inequality Theorem
Do the practice problems included with above video

Chapter Review pg. 317#1-18

Unit 6 G.6 Congruent Triangles

G.6 given information in the form of a figure or statement, will prove two triangles are congruent.

Video on Triangle Congruence Theorems

Practice on SSS and SAS

Practice on SSS,ASA,AAS,SAS congruence

Chapter Review pg. 263#1-25

Unit 7  G.7 Similar Triangles

G.7 given information in the form of a figure or statement, will prove two triangles are similar

Triangle similarity postulates
Video

Practice

Chapter review pg. 417 #1-15

Unit 8 G.8 b,c Right Triangles and Special Right Triangles

G.8 solve problems, including practical problems, involving right triangles. This will include applying
a) the Pythagorean Theorem and its converse

b) properties of special right triangles

c) trigonometric ratios

d) the Pythagorean Theorem and its converse

Video on Special Right Triangles

Trigonometry!

Chapter review pg. 465#1-39

Unit 9 G.9 & G.10 abc  Quadrilaterals and Polygons

G.4 construct and justify the constructions of

h) an equilateral triangle, a square, and a regular hexagon inscribed in a circle

G.9 verify and use properties of quadrilaterals to solve problems, including practical problems

G.10 solve problems, including practical problems, involving angles of convex polygons. This will include determining the

a) sum of the interior and/or exterior angles

b) measure of an interior and/or exterior angle

c) number of sides of a regular polygon

Constructions of a Square, equilateral Triangle and a regular hexagon in a circle
Video (this we haven't practiced) - try it on Desmos

Chapter Review Pg. 375#1-20

COVID 19 interrupts  instruction

What we have not covered: yet

2-D Figures- Area, Perimeter and Similarity-4 days
3-D Figures- 4 days
Symmetry - 1 day
Tessellations- 1 day
Transformations - 2 day