Program Guide - Department of Human Resources, Labour and ...

IM 3221
Advanced Geometry II
1. Ratio, Proportion, and Similarity
1.1 State ratios in simplest forms.
1.2 Apply properties of proportions to derive an equivalent proportion.
1.3 Apply properties of proportions to solve for an unknown in a proportion.
1.4 State properties of similar polygons.
1.5 State postulates and theorems for similar triangles.
1.6 Apply postulates and theorems to find unknown sides and angles in similar
polygons.
1.7 Apply postulates and theorems to prove polygons similar.
1.8 State and prove Triangle Proportionality Theorem with its corollary and
Triangle Angle-Bisector Theorem.
1.9 Use Triangle Proportionality Theorem, its corollary, and Triangle Angle-
Bisector Theorem to determine unknown proportional line segments and
unknown sides of triangles.
2. Right Triangles and Trigonometry
2.1 Determine geometric means between two numbers.
2.2 State theorems and corollaries related to right triangles and apply them to
determine length of various sides of right triangles.
2.3 State and prove Pythagorean Theorem.
2.4 Apply Pythagorean Theorem to determine various sides of right triangles.
2.5 State converse of the Pythagorean Theorem and other theorems related to
right triangles.
2.6 State theorems related to special triangles of 45 - 45 - 90 and 30 - 60 - 90 and
apply them to finding sides of various sides of right triangles.
2.7 Define sine, cosine, and tangent ratio of a right triangle.
2.8 Apply sine, cosine, and tangent to determine sides of triangles.
2.9 Apply sine, cosine, and tangent to solve distances in word problems.
3. Circles
3.1 Define terms related to circle and sphere.
3.2 Identify inscribed polygons and circumscribed circles.
3.3 State theorems related to tangents and radii and apply these theorems to
writing proofs and determining lengths of tangents and radii.
3.4 Define terms related to arcs and central angles.
3.5 State and apply theorems about chords of a circle and apply them to writing
161
ABE Level III Curriculum