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21st Century Learning Mathematics Standard

J.O. Combs Unified School District #44

High School: Honors Geometry

Honors Geometry explores mathematical concepts at a faster pace and a greater depth than Geometry.

Students in this course will study a greater breadth of geometric concepts and a more formalized approach to

proof-writing than students in Geometry. This rigorous course is designed to prepare students who excel in

mathematics for future honors courses.

1. LOGIC

• HGEO.1.1 Writes converse, inverse, contrapositive, and biconditional (as applicable) of a conditional

statement (required: statements and symbols).

• HGEO.1.2 Writes conclusions using laws of syllogism, detachment, contrapositive, and indirect

reasoning (required: statements and symbols).

• HGEO.1.3 Uses deductive reasoning to construct a 2-column proof.

• HGEO.1.4 Writes indirect proofs.

2. POINTS, SEGMENTS, LINES, AND PLANES

• HGEO.2.1 Applies postulates and theorems to make conclusions about segments, lines, and planes.

• HGEO.2.2 Applies postulates and theorems to calculate midpoint and lengths of segments (required:

midpoint formula and distance formula).

• HGEO.2.3 Writes the equation of parallel and perpendicular lines given critical information.

3. ANGLES

• HGEO.3.1 Applies postulates and theorems to find unknown angle measures.

• HGEO.3.2 Applies postulates and theorems to make conclusions about angles and their relationships

4. TRIANGLE CONGRUENCE

• HGEO.4.1 Uses congruence postulates and theorems to identify congruent triangles.

• HGEO.4.2 Uses congruence postulates and theorems to prove congruent triangles.

5. SIMILARITY

• HGEO.5.1 Uses similarity postulates and theorems to identify similar polygons.

• HGEO.5.2 Uses similarity postulates and theorems to make conclusions about similar polygons.

• HGEO.5.3 Uses similarity theorems to find lengths, perimeters, areas and volumes in similar figures.

6. POLYGONS

• HGEO.6.1 Differentiates quadrilaterals based on the definition.

• HGEO.6.2 Applies postulates and theorems to find unknown angle measures and segment lengths

(required: triangles, quadrilaterals, and regular polygons).

• HGEO.6.3 Applies postulates and theorems to make conclusions about polygons (required: triangles

and quadrilateral).

7. RIGHT TRIANGLES

• HGEO.7.1 Applies the Pythagorean Theorem to find unknown side lengths.

• HGEO.7.2 Calculates unknown side lengths of special right triangles (required: 30-60-90 and 45-45-

90).

• HGEO.7.3 Calculates unknown side lengths and angles measures of right triangles using

trigonometric ratios.

• HGEO.7.4 Sets up, solves, and analyzes right triangle application problems.

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8. CIRCLES

• HGEO.8.1 Uses the properties and postulates to find unknown arc lengths, angles, and arc measures.

• HGEO.8.2 Graphs a circle from h k form.

• HGEO.8.3 Writes the equation of a circle given a graph or critical information.

9. PERIMETER AND AREA

• HGEO.9.1 Calculates the perimeter of planar figures.

• HGEO.9.2 Calculates the area of planar figures.

10. SURFACE AREA

• HGEO.10.1 Calculates surface area of a three-dimensional figure.

• HGEO.10.2 Applies geometric principles to a real life situation (required: surface area).

• HGEO.10.2 Sketches nets of figures and identifies figures from their nets.

11. VOLUME

• HGEO.11.1 Calculates the volume of a three-dimensional figure.

• HGEO.11.2 Applies geometric principles to a real life situation (required: volume).

12. OBLIQUE TRIANGLE TRIGONOMETRY

• HGEO.12.1 Solves triangles (required: oblique law of sines and cosines and the ambiguous case).

• HGEO.12.2 Solves application problems of oblique triangles (required: bearings).

13. TRANSFORMATIONAL GEOMETRY

• HGEO.13.1 Transforms an image.

• HGEO.13.2 Differentiates between translations, rotations, and reflections, giving the reflection line or

the direction and angle of rotation, as applicable.

• HGEO.13.3 Describes translations and reflections using coordinate notation.

• HGEO.13.4 Uses rotation and translation theorems to make conclusions about transformations

14. ORGANIZING AND ANALYZING DATA

• HGEO.14.1 Displays data in an appropriate graphical representation.

• HGEO.14.2 Calculates measures of central tendency (required: mean, median, and mode).

• HGEO.14.3 Calculates measures of variation (required: standard deviation).

15. PROBABILITY AND COUNTING RULES

• HGEO.15.1 Calculates and analyzes the probability of events (required: addition rule and

multiplication rule).

• HGEO.15.2 Calculates and analyzes the probability of "at least"/"at most" events (required:

complements).

• HGEO.15.3 Calculates and analyzes the probability of events involving counting rules (required:

permutations, combinations, counting principle, and factorials).

• HGEO.15.4 Uses permutations and combinations to determine number of total outcomes.