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New YorkMaths

Geometry: Similarity, Trigonometry, and Circles

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do central and inscribed angles relate to arcs, and how do you work with arc length, sectors, and the equation of a circle?

Apply central angle, inscribed angle, chord, tangent, and secant relationships in a circle; compute arc length and sector area; and write and use the equation of a circle in the coordinate plane.
A NY Regents Geometry answer on circles: central and inscribed angles, the chord, tangent, and secant relationships, arc length and sector area, and the standard equation of a circle on the coordinate plane.
9 min answer →

How do you use distance, midpoint, slope, and partitioning to analyze figures on the coordinate plane?

Use the distance, midpoint, and slope formulas to analyze figures; determine parallel and perpendicular lines from slope; partition a directed segment into a given ratio; and write equations of lines satisfying given conditions.
A NY Regents Geometry answer on coordinate geometry: the distance, midpoint, and slope formulas, parallel and perpendicular slope conditions, partitioning a segment in a ratio, and writing equations of lines.
9 min answer →

How does a dilation change a figure, and how do you prove two figures similar?

Perform dilations on the coordinate plane and describe their effect on lengths and angles; define similarity through a sequence of rigid motions and a dilation; and prove triangles similar using AA (and SAS, SSS similarity), then use proportions to find missing lengths.
A NY Regents Geometry answer on dilations and similarity: performing a dilation about a center, why angles are preserved while lengths scale, the AA similarity criterion, and using proportions to find missing sides.
9 min answer →

How do the sine, cosine, and tangent ratios let you find missing sides and angles in a right triangle?

Define the sine, cosine, and tangent ratios in a right triangle (SOHCAHTOA), use them with inverse trig functions to find missing sides and angles, apply the relationship between the sine and cosine of complementary angles, and solve angle-of-elevation and depression problems.
A NY Regents Geometry answer on right triangle trigonometry: the sine, cosine, and tangent ratios, inverse trig to find an angle, the complementary sine-cosine relationship, and angle of elevation and depression problems.
9 min answer →

How do you find the volume of solids, identify cross sections and solids of revolution, and apply density?

Use volume formulas for prisms, cylinders, pyramids, cones, and spheres; identify the two-dimensional cross sections of three-dimensional solids and the solids formed by rotating a region; and solve density problems combining volume with mass or population.
A NY Regents Geometry answer on volume and solids: the prism, cylinder, pyramid, cone, and sphere formulas, identifying cross sections and solids of revolution, and applying density to mass and population problems.
9 min answer →