Objective 001
G-CO.1
Geometry
High School Geometry Practice Problems
Transformations, proof, similarity, trigonometry, coordinate geometry, circles, measurement, and probability.
57 objectives
Objective 002
G-CO.12
Perform formal constructions with compass/straightedge, paper folding, string, reflective devices, or geometry software.
Objective 003
G-CO.13
Construct an equilateral triangle, square, and regular hexagon inscribed in a circle.
Objective 004
G-CO.2
Represent transformations as functions on points and compare distance/angle-preserving transformations with non-rigid transformations.
Objective 005
G-CO.3
Describe rotations and reflections that carry rectangles, parallelograms, trapezoids, or regular polygons onto themselves.
Objective 006
G-CO.4
Define rotations, reflections, and translations using geometric language: angles, circles, perpendicular/parallel lines, and segments.
Objective 007
G-CO.5
Draw transformed figures and specify transformation sequences mapping one figure to another.
Objective 008
G-CO.6
Use rigid motions to transform figures and decide whether two figures are congruent.
Objective 009
G-CO.7
Use rigid motions to show triangle congruence through corresponding sides and angles.
Objective 010
G-CO.8
Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.
Objective 011
G-CO.10
Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.
Objective 012
G-CO.11
Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Objective 013
G-CO.9
Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Objective 014
G-SRT.1.a
Verify that dilations send non-center-passing lines to parallel lines and leave center-passing lines unchanged.
Objective 015
G-SRT.1.b
Verify that dilations scale line segments by the dilation scale factor.
Objective 016
G-SRT.2
Use similarity transformations to decide similarity and explain angle equality and side proportionality in triangles.
Objective 017
G-SRT.3
Use similarity transformations to establish the AA similarity criterion.
Objective 018
G-SRT.4
Prove triangle-similarity theorems, including proportional segments and the Pythagorean Theorem via similarity.
Objective 019
G-SRT.5
Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Objective 020
G-SRT.6
Define trigonometric ratios for acute angles using right-triangle similarity.
Objective 021
G-SRT.7
Explain and use the complementary-angle relationship between sine and cosine.
Objective 022
G-SRT.8
Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Objective 023
G-SRT.8.1
Derive and use trig ratios for 30-60-90 and 45-45-90 special right triangles.
Objective 024
G-SRT.10
Prove the Laws of Sines and Cosines and use them to solve problems.
Objective 025
G-SRT.11
Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.
Objective 026
G-SRT.9
Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.
Objective 027
G-GPE.4
Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Objective 028
G-GPE.5
Prove and use slope criteria for parallel and perpendicular lines.
Objective 029
G-GPE.7
Use coordinate methods to compute polygon perimeters and areas of triangles/rectangles.
Objective 030
G-GPE.1
Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Objective 031
G-GPE.2
Derive the equation of a parabola from a focus and directrix.
Objective 032
G-GPE.4
Use coordinates to prove simple geometric theorems, including simple circle theorems.
Objective 033
G-GPE.6
Find the point that partitions a directed segment between two points in a given ratio.
Objective 034
G-C.1
Prove that all circles are similar.
Objective 035
G-C.2
Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.
Objective 036
G-C.3
Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.
Objective 037
G-C.4
Construct a tangent line from an external point to a circle.
Objective 038
G-C.5
Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.
Objective 039
G-GMD.1
Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Objective 040
G-GMD.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Objective 041
G-GMD.5
Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.
Objective 042
G-GMD.6
Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Objective 043
G-GMD.4
Identify cross-sections of 3D objects and solids generated by rotating 2D objects.
Objective 044
G-MG.1
Use geometric shapes, measurements, and properties to describe real-world objects.
Objective 045
G-MG.2
Apply density concepts based on area and volume in modeling situations.
Objective 046
G-MG.3
Use geometric methods to solve design problems under constraints such as cost, space, or ratios.
Objective 047
S-CP.1
Describe events as subsets of a sample space using unions, intersections, and complements.
Objective 048
S-CP.2
Determine event independence using P(A and B)=P(A)P(B).
Objective 049
S-CP.3
Understand conditional probability and connect independence to unchanged conditional probabilities.
Objective 050
S-CP.4
Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.
Objective 051
S-CP.5
Explain conditional probability and independence in everyday language and situations.
Objective 052
S-CP.6
Compute conditional probability as the fraction of one event's outcomes that also belong to another event.
Objective 053
S-CP.7
Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).
Objective 054
S-CP.8
Apply and interpret the general Multiplication Rule with conditional probability.
Objective 055
S-CP.9
Use permutations and combinations to compute probabilities of compound events and solve problems.
Objective 056
S-MD.6
Use probability to make fair decisions, such as lotteries or random selection.
Objective 057
S-MD.7