Geometry Strategies - Part I
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Geometry
Summary
Geometry on the ACT works best when you actively use diagrams to combine visual reasoning with logic. The strongest approach is to redraw figures, label given and deduced information, add helpful marks or lines, and shift between small details and larger shapes to solve problems efficiently.
- Geometry relies heavily on visual thinking, so every problem should be approached with a diagram, whether the test provides one or not.
- Redrawing a figure on scratch paper makes it easier to mark up the diagram with information from the text and with facts you infer yourself.
- Simple visual symbols speed up organization: a small square marks perpendicular lines, and arrows can mark parallel lines in your own work.
- Some problems become easier when you extend an existing line, add a new line, or assign variables to lengths and angles so algebra can help solve the figure.
- Complex diagrams should be dissected strategically by examining both the small parts and the larger overall shapes.
- A problem filled with many small triangles may be solved faster by focusing on one large triangle and applying the triangle angle sum of 180 degrees.
- The key habit is to look both big and small, since the same geometric properties can apply to figures at different scales within the same diagram.
Chapters
00:00
Use Diagrams as the Foundation of Geometry
00:33
Redraw and Label Figures for Better Reasoning
01:11
Add Lines and Variables to Unlock Solutions
01:30
Solve by Looking at the Whole Shape