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Geometry Power Standards
PS1 - Reasoning, Proof, and Congruency Apply inductive reasoning to make conjectures and develop
counterexamples to refute invalid conditional statements. Construct a viable argument to justify a solution method. Apply
triangle relationships to determine missing angle measures. Prove triangles congruent using SSS, SAS, ASA, AAS, and
HL.
● Recognize conditional statements
● Recognize congruent figures and their corresponding parts
● LT1: Apply inductive reasoning to make conjectures
● LT2: Write the converse of a conditional and determine their truth values. Develop counterexamples to refute
invalid conditional statements.
● LT3: Construct a viable argument to justify a solution method.
● LT4: Identify pairs of angles as complementary, supplementary, adjacent, or vertical, and apply these
relationships to determine missing angle measures
● LT5: Prove triangles congruent using SSS, SAS, ASA, AAS, and HL. Prove parts of two triangles congruent
using CPCTC.
PS2 - Parallel/Perpendicular Lines Know and apply theorems about parallel and perpendicular lines and angles,
including angles that arise from parallel lines intersected by a transversal. Determine the equation of a line in the
coordinate plane that is described geometrically, including a line through two given points, a line through a given point
parallel to a given line, and a line through a given point perpendicular to a given line.
● Given parallel lines cut by a transversal, identify corresponding, same-side interior, same-side exterior, alternate
interior, and alternate exterior angle pairs.
● Relate slope to parallel and perpendicular lines
● LT1: Apply theorems about parallel and perpendicular lines and angles that arise from parallel lines intersected
by a transversal.
● LT2: Graph linear functions and show intercepts and slope
● LT3: Determine the equation of a line in the coordinate plane that is described geometrically, including a line
through two given points, a line through a given point parallel to a given line, and a line through a given point
perpendicular to a given line.
PS3 Polygons Apply properties of triangle midsegments and inequalities related to angles/sides of triangles.
Differentiate polygons, relate their properties, and apply the relationships to solve problems.
● Classify polygons and special types of quadrilaterals
● LT1: Apply properties of triangle midsegments to solve problems
● LT2: Apply inequalities involving angles and sides of triangles
● LT3: Find the sums of measures of the interior angles of polygons
● LT4: Apply relationships among sides and among angles of parallelograms as well as relationship involving
diagonals (transversals) of a parallelogram. Determine whether a quadrilateral is a parallelogram.
● LT5: Apply properties of diagonals of rhombuses and rectangles. Determine whether a parallelogram is a
rhombus or rectangle.
● LT6: Verify and apply properties of trapezoids and kites
PS4 Similarity, Right Triangles & Trigonometry Identify and apply similar polygons, including the use of similarity
criteria for triangles to solve problems and to prove relationships in geometric figures. Differentiate and apply
relationships in similar right triangles. Apply the Pythagorean Theorem and its converse, relate special right triangles,
apply the trigonometric ratios to solve problems including angles of elevation and depression, and describe vectors.
● Write ratios and solve proportions
● LT1: Identify and apply similar polygons, including proving triangles similar using AA, SAS, and SSS similarity
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LT2: Apply the Side-Splitter and Triangle-Angle-Bisector Theorems, as well as the properties of perpendicular
and angle bisectors
LT3: Differentiate and apply relationships in similar right triangles
LT4: Interpret word problems to determine a solution strategy involving the application of Pythagorean Theorem,
Special Right Triangles, and Trigonometric Ratios, including angles of elevation and depression as well as
vectors
PS5 Transformations Identify and perform transformations to geometric figures in the plane that include: translations,
reflections, rotations, glide reflections, and dilations.
● Identify isometries
● LT1: Find translation and reflection images of figures
● LT2: Draw and identify rotation images of figures
● LT3: Identify the type of symmetry in a figure
● LT4: Locate dilation images of figures
● LT5: Apply a composition of reflections, including glide reflections
● LT6: Identify transformations and symmetries in tesselations, and figures that will tessellate
PS6 Area, Surface Area & Volume Develop and apply formulas to calculate area of polygons, including the use of
trigonometry to find area. Develop and apply formulas for the surface area and the volume of prisms, cylinders, pyramids,
cones, and spheres. Identify and apply the relationships between the ratios of perimeters, areas, and volumes in similar
figures.
● Recognize polyhedra and their parts
● LT1: Apply coordinates to compute perimeters and areas of rectangles
● LT2: Solve the area of polygons, including parallelograms, triangles, trapezoids, rhombuses, kites, and regular
polygons, using trigonometry when necessary
● LT3: Solve the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composite figures
● LT4: Apply the relationships between the ratios of the perimeters, areas, and volumes of similar figures
PS7 Circles Apply the properties of tangents, secants, chords, and arcs of circles. Distinguish between central angles,
inscribed angles, and angles formed by chords, secants, and tangents to solve problems. Apply coordinate geometry to
describe the standards form of an equation of a circle.
● Find the measures of central angles and arcs
● Finding the distance between two points in the coordinate plane
● Find the coordinates of the midpoint of a segment in the coordinate plane
● LT1: Solve circumference and arc length, as well as the area of circles, sectors, and segments of circles
● LT2: Apply the relationship between a radius and a tangent, as well as the relationship between two tangents
from one point
● LT3: Apply congruent chords, arcs, and central angles
● LT4: Find the measure of an inscribed angle and the measures of angles formed by chords, secants, and
tangents
● LT5: Find the lengths of segments associated with circles
● LT6: Identify the center and radius of a circle to write the equation of a circle
PS8 Constructions (Additional constructions will be added per Common Core)
● LT1: Use a compass and a straightedge to construct congruent segments and congruent angles
● LT2: Use a compass and a straightedge to bisect segments and angles
Proofs of theorems will be added per Common Core