Geometry · Honors

High school · Math

Curriculum programs

Click a standard for the full text and study materials.

1.1 — Construct bisectors and parallel lines. Construct perpendicular bisectors, angle bisectors, and parallel lines using geometric tools.
1.2 — Regular figures. Identify and describe properties of regular polygons and related figures.
1.3 — Rigid motions. Perform and describe translations, rotations, and reflections without relying on a grid.
1.4 — Congruence via rigid motions. Define congruence as a sequence of rigid motions taking one figure onto another.
1.5 — Introduction to proof. Write informal and narrative proofs using definitions, postulates, and recorded theorems.
1.6 — Formal transformation proofs. Write point-by-point proofs that a sequence of rigid motions establishes congruence.

2.1 — Apply triangle congruence criteria. Apply ASA, SAS, SSS, and AAS criteria to prove triangles congruent.
2.2 — HL congruence. Use the hypotenuse-leg criterion to prove right triangles congruent.
2.3 — Use corresponding parts of congruent triangles in proofs. Use corresponding parts of congruent triangles to justify geometric conclusions in proofs.
2.4 — Geometric constructions. Use a compass and straightedge to create and justify standard geometric constructions.
2.5 — Proofs about quadrilaterals. Prove properties of parallelograms, rectangles, rhombi, and squares.
2.6 — Isosceles and equilateral triangles. Prove and apply base-angle and equilateral triangle theorems.
2.7 — Two-column and flowchart proofs. Organize multi-step congruence arguments in two-column or flowchart form.

3.1 — Dilations and scale factor. Perform dilations; relate scale factor to corresponding lengths.
3.2 — Apply AA and SAS similarity. Apply AA and SAS similarity criteria to establish that triangles are similar.
3.3 — SSS similarity. Use proportional corresponding sides to establish triangle similarity by SSS.
3.4 — Solve problems with parallel lines. Use angle relationships formed by parallel lines and transversals to solve problems.
3.5 — Proportional segments in triangles. Use parallel lines and similarity to establish proportional segments within triangles.
3.6 — Use altitude to the hypotenuse. Use similarity relationships created by an altitude to a right triangle's hypotenuse.
3.7 — Prove the Pythagorean theorem via similarity. Prove the Pythagorean theorem using relationships among similar triangles.
3.8 — Prove AA and SAS similarity. Prove the AA and SAS criteria for triangle similarity from geometric definitions and theorems.
3.9 — SSS similarity from the definition of similarity. Derive the SSS similarity criterion from the definition of triangle similarity.

4.1 — Define sine and cosine. Define sine and cosine using side ratios in right triangles.
4.2 — Tangent for acute angles in right triangles. Define and apply the tangent ratio for acute angles in right triangles.
4.3 — Solving right triangles. Find missing sides and angles using trig ratios and inverse trig.
4.4 — Angles of elevation and depression. Model and solve application problems involving elevation and depression.
4.5 — Use 30-60-90 triangles. Use 30-60-90 triangle side relationships to find unknown lengths.
4.6 — 45-45-90 relationships with trig ratios. Use 45-45-90 triangle relationships with trigonometric ratios to find unknown side lengths.

5.1 — Describe cross sections. Describe the two-dimensional cross sections formed by slicing three-dimensional solids.
5.2 — Volume. Derive and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres.
5.3 — Surface area. Compute surface area of prisms, cylinders, pyramids, and cones.

6.1 — Use the distance formula. Use the distance formula to find lengths and verify geometric relationships.
6.2 — Midpoint formula. Use the midpoint formula to find a segment's midpoint or a missing endpoint.
6.3 — Write equations of parallel lines. Write equations of lines parallel to a given line through a specified point.
6.4 — Perpendicular lines. Use slopes and angle relationships to identify and write equations of perpendicular lines.
6.5 — Equations of circles. Write and graph circle equations from center-radius form.
6.6 — Prove triangle properties with coordinates. Use coordinate methods to prove properties of triangles.
6.7 — Quadrilateral properties using coordinates. Use slopes, distances, and midpoints to prove properties of quadrilaterals.

7.1 — Relate central angles and arcs. Relate the measure of a central angle to the measure of its intercepted arc.
7.2 — Inscribed angles and intercepted arcs. Relate inscribed angles to their intercepted arcs.
7.3 — Apply chord and tangent theorems. Apply circle theorems involving chords and tangents to determine lengths and angles.
7.4 — Angles formed by secants. Find angle measures formed by secants intersecting inside or outside a circle.
7.5 — Compute arc length. Calculate the length of a circular arc from its radius and central angle.
7.6 — Sector area. Calculate the area of a circular sector from its radius and central angle.
7.7 — Apply power-of-a-point relationships. Use power-of-a-point relationships to solve problems involving intersecting chords and secants.
7.8 — Tangents to circles. Apply properties of tangent lines, radii, and tangent segments in circle problems.

8.1 — Find probabilities from two-way tables. Use two-way tables to find probabilities of unions, intersections, and complements.
8.2 — Sample spaces. List outcomes and describe sample spaces for chance experiments.
8.3 — Identify independent events. Determine whether two events are independent by comparing conditional and unconditional probabilities.
8.4 — Interpret conditional probabilities. Interpret conditional probabilities in context and distinguish them from joint probabilities.