Measurement
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 
 VDOE Enhanced Scope and Sequence Lesson: Similar Figures (PDF)  Determining whether two plane figures are similar, identifying corresponding sides (Word)
 Notes: Similar Figures (flipchart)
 Notes: Similar Figures #2 (flipchart)
 Notes: Determining Similar Figures (flipchart)
 Activity: Determining Similar Figures (flipchart)
 VDOE Algebra Readiness Curriculum Companion: Working with Polygons (pdf)
 VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions (pdf)

Real World Lessons 

Practice 
 VDOE ESS: Similar Figures Activity (pdf)
 Worksheet: Similar Figures CW (doc)
 Worksheet: Similar Figures HW (doc)
 Worksheet: Simple Similarity (doc)
 Quiz: Similar Figures (doc)

SOL Mini Quiz 
 SOL 7.6 Mini Quiz: Similar Figures (pdf)  (doc)

Skills 
 Similar Figures: Floor Plans (doc)

Videos 
 YouTube: Similar Figures and Proportions
 YouTube: Similar Figures
 Virtual Nerd: What are Similar Figures?
 Virtual Nerd: Similar Figures and Missing Measurements
 PH: Using similar figures to find indirect measurement
 PH: Using proportion to find unknown length in similar figures

Explore
Learning 
 Similar Figures  Activity A: Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related.

Websites 
 IXL: Create Histograms

VDOE Interventions 
 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)
 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 
