Math Trick 2: Multiplying 2 Digit Numbers Numbers by 11

In the previous post, we learned a cool math trick on squaring numbers (positive integers) ending in 5. We did not only learn the math trick itself, but we also discussed why it works. In this post, we will explore another math trick which is multiplying 2 digit numbers by 11.

The Copy-Add-Copy Method

To multiply 2 digit numbers by 11, we will use the copy-add-copy method. We will copy and add the digits of the number multiplied by 11. Below are the steps of this method.

Steps in Multiplying 2-Digit Numbers by 11

  1. Copy the ones digit of the number multiplied by 11 to the ones digit of the product.
  2. Add the ones digit and the tens digit of the number and copy the sum (see *) to the tens digit of the product.
  3. Copy the tens digit of the number (see **) to the hundreds digit of the product. Continue reading

SSS Congruence Theorem and Its Proof

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. Continue reading

A Practical Demonstration of the Pythagorean Theorem

The Pythagorean Theorem is probably the most popular theorem in school mathematics. Surely, you have heard or read about it at least once from elementary school to high school. The Pythagorean Theorem states that given a right triangle with shorter sides a, b, and hypotenuse c, the following equation holds

c^2 = a^2 + b^2.

The Pythagorean Theorem

 

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