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Corresponding angles are equal.

If Corresponding angles are equal then the lines are parallel.

1.1 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals, and parallel lines, with or without technology.

1.5 Verify, using examples, that if lines are not parallel the angle properties do not apply.

Questions 2, 3 and 5a and d – Page 72

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In parallel lines intersected by a transversal:

Corresponding angles are equal.

Alternate interior angles are equal

Alternate exterior angles are equal.

The Acute angles and Obtuse angles are Supplementary.

1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.

1.4 Identify and correct errors in a given proof of a property involving angles.

2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning.

2.2Identify and correct errors in a given solution to aproblem that involves the measures of angles.

2.3 Solve a contextual problem that involves angles or triangles.

2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used.

2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.

Questions 3e, f, g and h, 4b and c, 8, 12,15, and 16 on Pages79 - 81

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You can prove properties in triangles using other angle properties that have been already proven.

The angles in a triangle add up to 180 degrees.

The measure of any exterior angle of a triangle is proven to be equal to the sum of the measure to the two non-adjacent interior angles.

1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.

2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning.

2.2Identify and correct errors in a given solution to aproblem that involves the measures of angles.

2.3Solve a contextual problem that involves angles or triangles.

Questions 2, 5, 6, 9, 12 (Key Question), and 15

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You can prove properties in polygons using other angle properties that have been already proven.

Sum of the measures of the interior angles of a convex polygon =

Measure of each angle of a regular polygon =

The sum of the measure ofthe exterior angles of any convex polygon is 360 degrees.

1.3 Generalize, using inductive reasoning, a rule for the relationship between the sum of the interior angles and the number of sides (n) in a polygon, with or without technology.

1.4 Identify and correct errors in a given proof of a property involving angles.

2.2Identify and correct errors in a given solution to aproblem that involves the measures of angles.

2.3Solve a contextual problem that involves angles or triangles.

#4, 7, 10 (Key Question),, 11, 18

Resources:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=9Might help with this concept

http://regentsprep.org/Regents/math/geometry/GG3/JavaIntAngles.htmThis applet my help start discussions of the interior angles of a polygon

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There are minimum sets of angle and side measurements that, if known, allow you to conclude that two triangles are congruent.

SAS

SSS

ASA

1.6 Prove, using deductive reasoning, that two triangles are congruent.

1a and b, 2a, and 3a and b

Resources:

http://www.onlinemathlearning.com/congruent-triangles.htmlGreat notes with supporting videos and worked out examples.

http://staff.argyll.epsb.ca/jreed/math9/strand3/triangle_congruent.htmIf you scroll down you will see an applet on Congruent triangles

http://www.mathopenref.com/congruentaaa.htmlApplet on showing why AAA does not work to prove that triangles are congruent

http://www.mathopenref.com/congruentssa.htmlApplet on showing why SSA does not work to prove that triangles are congruent

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To show that two triangles are congruent, then you must show that corresponding sides and angles are congruent.

1.6 Prove, using deductive reasoning, that two triangles are congruent.2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning.

2.2Identify and correct errors in a given solution to aproblem that involves the measures of angles.

2.3Solve a contextual problem that involves angles or triangles.

4, 8, 9 (key question), 11, 17, and 18

Resources:

http://www.youtube.com/watch?v=NAhcmPS5k9gVideo from Yourteacher.com

http://library.thinkquest.org/20991/geo/ctri.htmlGreat notes

http://www.wikihow.com/Write-a-Congruent-Triangles-Geometry-ProofHow to werite a Congruent Triangles Proof