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Praxis Geometry study materials
Praxis Geometry study resources

Praxis Geometry: Geometry Content Knowledge

Praxis Geometry · Work through your exam, one topic at a time.

All guide sections

Geometry Content Knowledge

What this domain tests

The Geometry content knowledge domain of the Praxis Geometry exam assesses your ability to reason with Euclidean and coordinate geometry, justify claims with proofs, and apply transformations, similarity, congruence, circles, measurement, and right-triangle trigonometry. Questions often ask not only for a numerical answer but for the theorem or definition that makes the answer valid.

Core rules to know cold

  • Congruence: SSS, SAS, ASA, AAS, and HL for right triangles. SSA and AAA are not congruence criteria.
  • Similarity: AA, SSS similarity, and SAS similarity. A dilation with scale factor k multiplies lengths by k and area by k²; volumes scale by k³.
  • Transformations: translations, rotations, and reflections are rigid motions and preserve congruence; dilations preserve angle measure and shape but not length.
  • Circles: an inscribed angle is half the central angle on the same arc; a radius perpendicular to a tangent meets it at the point of tangency; a perpendicular from the center to a chord bisects the chord; opposite angles of a cyclic quadrilateral are supplementary.
  • Coordinate tools: distance, midpoint, slope, parallel/perpendicular slope relationships, and equations of circles (x−h)²+(y−k)²=r².
  • Right triangles: Pythagorean theorem and the ratios sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent.

Worked example

Two similar triangles have corresponding sides 5 cm and 8 cm. The smaller triangle’s area is 30 cm². Find the larger area. The linear scale factor is 8/5, so the area scale factor is (8/5)² = 64/25. Multiply: 30 × 64/25 = 76.8 cm². The key reasoning is that area scales by the square of the linear scale factor, not by 8/5.

Traps that cost marks

Do not use SSA as a congruence shortcut. Do not apply the inscribed-angle theorem to angles that intercept different arcs. Check whether a diameter, radius, or chord is given before using circle formulas. In similarity problems, match corresponding vertices before writing ratios. When a proof is requested, cite the definition, postulate, or theorem by name rather than only giving the calculation.