Geometry Success is Very Accessible for Your High School Math Student

High school geometry has two different goals that make this course fundamentally different from all the other high school math courses.

Goals for this Course
The first goal is that the student should learn the properties of plane and solid figures. An example of this is the Pythagorean Theorem, a property of right triangles.

Will learning skills in geometry help my child in real life?

Yes! Your child will learn the skill of mathematical reasoning, which isn't emphasized in the other high school math courses because it is not as accessible there as it is in geometry.

In some less rigorous courses, the proof aspect is de-emphasized. Also in some courses, more contemporary approaches, such as transformational geometry, are introduced.

This will develop a basis for critical reasoning and deductive thinking skills that every adult needs in life.

What the Student Should Achieve

The overall goal of the student is to understand and retain the many definitions, theorems and formulas of geometry and also, in a deductive course, learn how to write mathematical proofs.

By the way, many parents are not really certain why their child needs to learn math at all. If you can't confidently answer why your child should learn high school math, please read my article, "Why Your Child Needs a Good High School Math Education."

When to Get Extra Help
If the course homework gets too hard for your student (and you) to complete in a reasonable amount of time, extra help outside the classroom may be necessary. There are great software products like Geometry Solved! which may be more user friendly than a workbook for a teenager!

It's very important for your child "get the hang" of geometric thought and techniques now, while the concepts are more concrete. This will, in turn, ready your child for the more abstract concepts to come later in the course and in his or her math education career.

Investing in math skills enrichment, like the courses offered by Kumon (pronounced koo-Mohn), an after-school program or a private tutor may be well worth the time and money you'll spend.

It's important to lighten things up sometimes, so I wrote up some of my favorite Geometry Jokes that I've collected throughout my many years teaching this course. Pepper a few jokes into your child's day to help relieve tension.

Key Course Topics Should Include:

1. Reasoning skills: deduction, induction, indirect proof, the axiomatic method and formal systems. The terms conditional statement, converse, contrapositive and inverse; Venn diagrams. The students will learn the proofs of the theorems and also write their own proofs.
2. Points, lines, planes and angles: definitions and properties of these basic geometric figures; also segments, rays, distance, algebraic properties, special pairs of angles and theorems about perpendicular lines.
3. Parallel lines: properties of parallel lines; proving lines parallel; angles of a triangle; angles of a polygon.
4. Congruent triangles: SSS, SAS, ASA, AAS, and HL congruence schemes; using congruent triangles in proofs; theorems about isosceles triangles; proofs with more than one pair of congruent triangles; medians, altitudes and perpendicular bisectors.
5. Quadrilaterals: properties of parallelograms; proving a quadrilateral is a parallelogram; theorems involving parallel lines; special parallelograms and trapezoids.
6. Inequalities in triangles: properties of inequalities; theorems about inequalities in one and two triangles.
7. Similar polygons: ratio and proportion; properties of proportions; similar polygons and theorems about similar triangles; proportional lengths.
8. Right triangles: similarity in right triangles; the Pythagorean Theorem and its converse; special right triangles; right triangle trigonometry and its applications.
9. Circles: properties of tangents, arcs, central angles, chords, inscribed angles and other angles; circles and segment lengths.
10. Constructions: constructions involving perpendicular and parallel lines, concurrent lines, circles, and special segments; locus problems.
11. Area of plane figures: squares; rectangles; parallelograms; triangles; rhombuses; trape-zoids; regular polygons; circles; sectors; circumference of circles and arc length; ratio of areas and geometric probability.
12. Volume and surface of solids: prisms; pyramids; cylinders; cones; spheres; ratio of areas and volumes of similar solids.
13. Coordinate Geometry: distance, slope, midpoint, linear equations.

Here is a helpful web site that will help you recall properties, theorems and formulas related to the geometric solids.

Learn more about the Pythagorean Theorem .

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