Week 1, Session 1: GED® Geometry Orientation, Formula Sheet, Units, and Calculator Readiness
Week 1, Session 2: Perimeter of Polygons and Real-World Boundary Problems
Week 2, Session 1: Area of Rectangles, Triangles, and Parallelograms
Week 2, Session 2: Polygons, Trapezoids, and Missing Dimensions
Week 3, Session 1: Circles—Radius, Diameter, Circumference, and Area
Week 3, Session 2: Composite 2-D Figures and Shaded Regions
Week 4, Session 1: Unit Conversions, Scale Drawings, Maps, and Blueprints
Week 4, Session 2: Similar Figures and Proportional Geometry
Week 5, Session 1: Pythagorean Theorem Foundations
Week 5, Session 2: Pythagorean Applications and Distance on a Grid
Week 6, Session 1: Volume of Rectangular Prisms and Triangular Prisms
Week 6, Session 2: Volume of Cylinders, Cones, Pyramids, and Spheres
Week 7, Session 1: Surface Area of Prisms and Cylinders
Week 7, Session 2: Surface Area of Pyramids, Cones, Spheres, and Nets
Week 8, Session 1: Composite 3-D Solids and Real-World Design Problems
Week 8, Session 2: Coordinate Plane Foundations—Points, Quadrants, and Distances
Week 9, Session 1: Slope from Graphs, Points, Tables, and Contexts
Week 9, Session 2: Parallel and Perpendicular Lines
Week 10, Session 1: Linear Equations and Graphing in Geometry Contexts
Week 10, Session 2: Coordinate Geometry—Area, Perimeter, and Diagonal Distance on the Grid
Week 11, Session 1: Working Backward with Geometry Formulas
Week 11, Session 2: Multi-Step GED® Geometry Word Problems and Formula Selection
Week 12, Session 1: Timed Mixed GED® Geometry Practice and Error Analysis
Week 12, Session 2: Final GED® Geometry Review and Test-Day Strategy

Free trial session

Week 4, Session 2: Similar Figures and Proportional Geometry

GED® Advanced Geometry: Measurement, Coordinate Geometry, and Test-Day Problem Solving · preview lesson

Week 4, Session 2: Similar Figures and Proportional Geometry

Self-study purpose

Similar figures have the same shape but not necessarily the same size. GED® problems use similar triangles and rectangles to ask for missing lengths, scale factors, perimeters, and areas.

What you should be able to do after this session

Set up proportions from corresponding sides.
Find scale factor from one figure to another.
Use scale factor for perimeter and area relationships.
Recognize when two figures are similar.

Visual model

Geometry diagram: Similar figures have equal angles and proportional sides

Formula and idea bank

Corresponding side ratio: \(\frac{\text{new side}}{\text{old side}}=k\).
Perimeter scale factor = \(k\).
Area scale factor = \(k^2\).
Similar figures have equal corresponding angles.

Teacher explanation

Match sides by position: shortest with shortest, longest with longest, base with base.
Write proportions vertically and consistently.
Area grows faster than length because area has two dimensions.

Worked example

A triangle with sides \(6,8,10\) is enlarged so the side corresponding to \(6\) becomes \(9\). The scale factor is \(\frac{9}{6}=1.5\), so the new sides are \(9,12,15\).

GED® problem-solving routine

Identify corresponding sides.
Compute the scale factor.
Multiply or divide every corresponding length by the scale factor.
Use \(k^2\) only for area.

Common mistakes to avoid

Pairing non-corresponding sides.
Using the area scale factor for side lengths.
Assuming figures are similar just because they look close.

Mastery check

Before moving to the next session, complete the 10 questions below without notes. Then correct every missed problem by writing: given information → formula → substitution → answer with units.

Quick Check

If the length scale factor is 4, what is the area scale factor?

Advanced Extension and Harder GED® Practice

Deeper idea

Similar figures preserve shape but not size. Corresponding sides have the same ratio. Perimeter uses the same scale factor as length. Area uses the square of the scale factor. If the figures are similar triangles, matching the correct sides is more important than the arithmetic.

Worked example: similar triangles with missing side

Two similar triangles have corresponding side lengths 9 and 15. Another side on the smaller triangle is 12. Find the corresponding larger side.

Scale factor from smaller to larger: \(15\div9=\frac53\).
Multiply the matching side: \(12\cdot\frac53=20\).
Larger side: 20.

Harder GED® challenge

Two similar rectangles have side ratio \(4:7\). The smaller rectangle area is \(96\text{ cm}^2\). The larger area is \(96\cdot(\frac74)^2=96\cdot\frac{49}{16}=294\text{ cm}^2\).

Advanced trap to watch

Do not add the difference between sides to every side unless the problem says the figures grew by a fixed amount. Similarity is multiplication, not addition.