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Henrico County Public Schools, Virginia
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As a result, many of the instructional notes, activities, and worksheets will be removed. Please download any files you wish to keep for future use.
7.6 - Similar Figures
Number, Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Focus: Proportional Reasoning

The student will determine whether plane figures—quadrilaterals and triangles—are similar and write proportions to express the relationships between corresponding sides of similar figures. 
Essential Knowledge and Skills 
  • Identify corresponding sides and congruent angles of similar figures using the traditional notation of curved lines for the angles.
  • Write proportions to express the relationships between the lengths of corresponding sides of similar figures.
  • Determine if quadrilaterals or triangles are similar by examining congruence of corresponding angles and proportionality of corresponding sides.
  • Given two similar figures, write similarity statements using symbols for triangles, angles, and segments. See Curriculum Guide or VDOE Framework for examples.
Essential Understandings
  • How do polygons that are similar compare to polygons that are congruent? Congruent polygons have the same size and shape. Similar polygons have the same shape, and corresponding angles between the similar figures are congruent. However, the lengths of the corresponding sides are proportional. All congruent polygons are considered similar with the ratio of the corresponding sides being 1:1.
Vertical Articulation
  • SOL 5.13ab - a) using plane figures will develop definitions of plane figures; b) investigate/describe results of combining/subdividing plane figures
  • SOL 6.12 - determine congruence of segments/angles/polygons
  • SOL 8.10ab - a) verify the Pythagorean Theorem; b) apply the Pythagorean Theorem
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Similar Figures (PDF) - Determining whether two plane figures are similar, identifying corresponding sides (Word)
  2. Notes: Similar Figures (flipchart)
  3. Notes: Similar Figures #2 (flipchart)
  4. Notes: Determining Similar Figures (flipchart)
  5. Activity: Determining Similar Figures (flipchart)
  6. VDOE Algebra Readiness Curriculum Companion: Working with Polygons (pdf)
  7. VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions (pdf)
Real World Lessons
  1. VDOE ESS: Similar Figures Activity (pdf)
  2. Worksheet: Similar Figures CW (doc)
  3. Worksheet: Similar Figures HW (doc)
  4. Worksheet: Simple Similarity (doc)
  5. Quiz: Similar Figures (doc)
SOL Mini Quiz
  1. SOL 7.6 Mini Quiz: Similar Figures (pdf) | (doc)
  1. Similar Figures: Floor Plans (doc)
  1. YouTube: Similar Figures and Proportions
  2. YouTube: Similar Figures
  3. Virtual Nerd: What are Similar Figures?
  4. Virtual Nerd: Similar Figures and Missing Measurements
  5. PH: Using similar figures to find indirect measurement
  6. PH: Using proportion to find unknown length in similar figures
Explore Learning
  1. Similar Figures - Activity A: Vary the scale factor and rotation of an image and compare it to the pre-image. Determine how the angle measures and side lengths of the two figures are related.
  1. IXL: Create Histograms
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Working with Polygons - The lessons focus on identifying, classifying, describing, and comparing plane figures. Students determine similarity and congruence of figures and work with transformations.(pdf)
  2. VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions - The lessons focus on the meaning of ratios and proportions. Students practice writing ratios and build on their knowledge of ratios to work with proportions. Using proportional reasoning to solve practical problems is a common element in this section. (pdf)
Common Core Standards