where students teach themselves
A comprehensive geometry curriculum
Geometry for School and Home
Objectives: Develop and apply a theorem for triangles having a line segment with endpoints on two sides that is parallel to the third side. Use the converse of the theorem to identify parallel line segments.
Objectives: Develop and apply a theorem for the lengths of line segments intercepted by paralllel lines on two transversals. Use the converse of the theorem to identify parallel lines.
Objectives: Draw dilations of polygons.
Objectives: Measure to compare angles and ratios of side lengths in the image and preimage of a dilation of a polygon. Find angle measures and write and solve proportions to find side lengths of an image in a dilation.
Objectives: Name similar polygons. Name the corresponding vertices, congruent angles, and ratios of lengths of sides of similar polygons. Write and solve proportions to find lengths of sides of similar polygons.
Objectives: Write and simplify the scale factor of similar polygons. Use the scale factor to calculate side lengths in similar polygons. Write and simplify scale factors in dilations.
Objective: Identify similar polygons by comparing angle measures and ratios of lengths of sides.
Objective: Develop and apply the SSS Triangle Similarity Postulate.
Objective: Develop and apply the SAS Triangle Similarity Postulate.
Objective: Develop and apply the AA Triangle Similarity Postulate.
Objective: Use the SSS, SAS, and AA postulates to justify triangle similarity and name similar triangles.
Objective: Complete and write proofs of similar triangles using flow chart and two column forms.
Objective: Complete and write proofs that use parallel line theorems to prove that triangles are similar.
Objective: Complete and write proofs that use similar triangles to prove that pairs of angles are congruent.
Objective: Complete and write proofs that use similar triangles to prove that lengths of segments are proportional.
Objectives: Name congruent angles to prove similar triangles using the AA postulate. Complete and solve proportions in triangles determined to be similar by the AA postulate.
Objective: Write and solve indirect measurement problems using the AA postulate to determine similar triangles
Objectives: Determine whether ratios of line segment lengths are proportional using cross-products. Using a given proportional relationship of line segment lengths, substitute and solve for an unknown length.
Objectives: Write and simplify ratios of lengths of line segments. Compare ratios by simplifying or converting to decimals.
Objectives: Develop and apply a theorem about proportional line segment lengths in triangles with an angle bisector. Use the converse of the theorem to identify angle bisectors.
Objectives: Develop and apply a geometric mean theorem for right triangles with an altitude to the hypotenuse.
Objectives: Identify and name corresponding medians, altitudes, and angle bisectors of similar triangles. Write and solve proportions to find lengths of altitudes, medians, and angle bisectors in similar triangles.
Objectives: Calculate the geometric mean for two numbers. Given a number and a geometric mean, calculate the other number.