Download Unit K: Similarity (11.1 – 11.7)

Unit K: Similarity (11.1 – 11.7)
□ I can solve a proportion algebraically.
□ I will set up a proportion to represent a word problem.
□ I will solve a proportion algebraically.
□ I can define and solve problems involving similar polygons.
□ I will explain the definition of similar polygons.
□ I will determine if two polygons are similar by comparing corresponding sides and angles.
□ I will find the values of missing angles and sides of similar polygons.
□ I can use triangle similarity conjectures to prove triangles are similar.
□ I will explain how AA~, SSS~, and SAS~ prove similar triangles.
□ I will use AA~, SSS~, and SAS~ to prove similar triangles.
□ I can use indirect measurement to solve problems.
□ I will draw diagrams to represent applied problems.
□ I will use information about the shadows of objects to solve applied problems.
□ I will use information about mirror distances and reflections to solve applied problems.
□ I can use special similar triangle properties to solve problems.
□ I will use the Proportional Parts Conjecture to find missing measurements of similar triangles.
□ I will use the Angle Bisector/Opposite Sides Conjecture to find measurements within a triangle.
□ I will find the geometric mean between two numbers.
□ I will recognize the similarity between triangles formed by an altitude drawn to the hypotenuse of
a right triangle.
□ I will use geometric mean and proportions to find the length of the altitude in a right triangle
using the segments of the hypotenuse formed by the altitude drawn to the hypotenuse.
□ I will use geometric mean and proportions to find the length of a leg in a right triangle using the
segments of the hypotenuse formed by the altitude drawn to the hypotenuse.
□ I can solve problems related to the areas and volumes of similar figures and solids.
□ I will explain the relationship between the areas of similar figures and the surface areas of
similar solids.
□ I will apply the Proportional Areas Conjecture to problems involving areas.
□ I will explain the relationship between the volumes of similar solids.
□ I will apply the Proportional Volumes Conjecture to problems involving volume.
□ I can solve problems involving the segments between parallel lines.
□ I will explain the relationship between the ratios of the parts into which parallel lines cut the sides
of a triangle.
□ I will apply the Parallel/Proportionality Conjecture to solve problems.
Key Vocabulary and Concepts
corresponding angles
corresponding sides
geometric mean
indirect measurement
proportion
ratio
scale factor
similar
similarity
Conjectures
Dilation Similarity Conjecture
AA Similarity Conjecture
SSS Similarity Conjecture
SAS Similarity Conjecture
Proportional Parts Conjecture
Online Textbook
http://math.kendallhunt.com
Angle Bisector/Opposite Sides Conjecture
Proportional Areas Conjecture
Proportional Volumes Conjecture
Parallel/Proportionality Conjecture
Extended Parallel/Proportionality Conjecture
classpass: elliott12
Online Resources
Video on Solving Proportions:
http://www.brightstorm.com/math/geometry/similarity/solving-proportions/
Information and Practice on Similar Polygons:
http://library.thinkquest.org/20991/geo/spoly.html
Video on Properties of Similar Polygons:
http://www.brightstorm.com/math/geometry/similarity/properties-of-similar-polygons/
Online Practice Identifying Similar and Congruent Polygons:
http://www.harcourtschool.com/activity/similar_congruent/
Video on Similarity Shortcuts:
http://www.brightstorm.com/math/geometry/similarity/similarity-shortcuts/
Video(s) on Indirect Measurement:
(a) http://www.brightstorm.com/math/geometry/similarity/indirect-measurement/
(b) http://virtualnerd.com/geometry/similarity/triangles/indirect-measurement-example
Video on Corresponding Parts of Similar Triangles:
http://www.brightstorm.com/math/geometry/similarity/corresponding-parts-of-similar-triangles/
Video on Angle Bisector/Opposite Side Conjecture:
http://www.brightstorm.com/math/geometry/similarity/angle-bisectors-and-opposite-side-ratios/
Video on Parallel/Proportionality Conjecture:
http://www.brightstorm.com/math/geometry/similarity/proportional-segments-between-parallel-lines/
Video on Similarity and Area Ratios:
http://www.brightstorm.com/math/geometry/similarity/similarity-and-area-ratios/
Video on Similarity and Volume Ratios:
http://www.brightstorm.com/math/geometry/similarity/similarity-and-volume-ratios/
Extension Exercises
Indirect Measurement Activities:
http://mysite.cherokee.k12.ga.us/personal/nicole_howard/site/Lists/Subject%203%20Homework/Attachments/46/Holt%20I
ndirect%20Measure%20(Similar%20Rt%20Triangles).pdf
Online Activity with Indirect Measurement:
http://math.kendallhunt.com/x3292.html