← Maths syllabus

United StatesMaths

Geometry

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you use angle relationships and triangle properties to find unknown angles and sides on the ACT?

Apply angle relationships (vertical, supplementary, parallel-line angles) and triangle properties (angle sum, exterior angle, isosceles and the triangle inequality) to find unknowns (Geometry).
An ACT Geometry answer on angle and triangle relationships: vertical and supplementary angles, angles formed by parallel lines and a transversal, the triangle angle sum, the exterior-angle rule, isosceles triangles and the triangle inequality, with worked ACT-style questions.
10 min answer →

How do you compute area, perimeter, surface area and volume of common shapes and solids on the ACT?

Compute the perimeter and area of triangles, rectangles, parallelograms, trapezoids and circles, and the surface area and volume of prisms, cylinders and other common solids (Geometry, Integrating Essential Skills).
An ACT Geometry answer on area, perimeter and volume: formulas for triangles, rectangles, parallelograms, trapezoids and circles, plus surface area and volume of prisms and cylinders, and composite-figure strategy, with worked ACT-style questions.
11 min answer →

How do you use circle formulas and the equation of a circle on the ACT?

Apply circle formulas for circumference, area, arc length and sector area, and use the standard equation of a circle to find its centre and radius (Geometry).
An ACT Geometry answer on circles: circumference and area, arc length and sector area as fractions of the whole, central angles, and the standard equation of a circle giving its centre and radius, with worked ACT-style questions.
10 min answer →

How do you use the distance, midpoint and slope formulas in the coordinate plane on the ACT?

Apply the distance, midpoint and slope formulas, identify parallel and perpendicular lines, and analyse figures placed in the coordinate plane (Geometry).
An ACT Geometry answer on coordinate geometry: the distance and midpoint formulas, slope and parallel and perpendicular lines, and using coordinates to analyse triangles and other figures, with worked ACT-style questions and common traps.
10 min answer →

How do you use the Pythagorean theorem and SOH-CAH-TOA to solve right triangles on the ACT?

Apply the Pythagorean theorem, the special right triangles, and the sine, cosine and tangent ratios (SOH-CAH-TOA) to find sides and angles of right triangles (Geometry).
An ACT Geometry answer on right triangles: the Pythagorean theorem, the 30-60-90 and 45-45-90 special triangles, common Pythagorean triples, and the sine, cosine and tangent ratios (SOH-CAH-TOA) for finding sides and angles, with worked ACT-style questions.
11 min answer →

How do you use similarity and congruence, including proportional sides and scale factors, on the ACT?

Identify similar and congruent figures, use proportional corresponding sides and equal corresponding angles, and apply scale factors to lengths, areas and volumes (Geometry).
An ACT Geometry answer on similarity and congruence: equal angles and proportional sides in similar figures, solving for an unknown side with a proportion, scale factor, and how scale factor affects area and volume, with worked ACT-style questions.
10 min answer →