High School Geometry Archives - Page 5 of 23

Paper Folding: How to Construct an Equiangular Triangle

July 3, 2013 GB High School Geometry, High School Mathematics

Paper folding or origami can be used to create intricate and stunning designs. In addition, paper folding can also be used to teach or learn mathematics. In this post, we use a square piece of paper to construct an equiangular triangle. After the construction, we prove that the triangle is equiangular.

Steps in Constructing an Equiangular Triangle

1. Cut a square piece of paper. For the sake of discussion, we label the square ABCD.

2. Fold at the center so that AB coincides with CD . Crease well, then unfold.

3. Select vertex and fold so that A falls on the center line and the crease passes through D. Unfold. » Read more

3 comments constructing an equiangular triangle, equiangular triangle, origami, paper folding, teach or learn mathematics

Semiregular Tessellations: Adventurous Ideas for Floor Tiling

June 22, 2013 GB High School Geometry, High School Mathematics

If you are planning to tile your your floor and want something different from the usual tiling which is usually made up of rectangles or squares, the following semiregular tessellations might give you some ideas.

In the first figure, the tessellation is made up of squares and octagons (8-sided polygons). » Read more

Leave a comment dodecagon rectangle tessellation, dodecagon square triangle tessellation, hexagon square triangle tessellation, hexagon triangle tessellation, octagon square tessellation, square triangle tessellation

SSS Congruence Theorem and Its Proof

June 17, 2013 GB High School Geometry, High School Mathematics, Problem Solving and Proofs

Many high textbooks consider the congruence theorems (SSS Congruence Theorem, SAS Congruence Theorem, ASA Congruence Theorem) as postulates. This is because their proofs are complicated for high school students. However, let us note that strictly speaking, in Euclidean Geomtery (the Geometry that we learn in high school), there are only five postulates and no others. All of other postulates mentioned in textbooks aside from these five are really theorems without proofs.

In this post, we are going to prove the SSS Congruence Theorem. Recall that the theorem states that if three corresponding sides of a triangle are congruent, then the two triangles are congruent.

Before proving the SSS Congruence theorem, we need to understand several concepts that are pre-requisite to its proof. These concepts are isometries particulary reflection and translation, properties of kites, and the transitive property of congruence. If you are familiar with these concepts, you can skip them and go directly to the proof. » Read more

2 comments properties of a kite polygon, sss congruence proof, sss congruence theorem, sss triangle congruence proof, transitive property of congruence, triangle congruence

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