Basic strategies and first problem

I like the R.U.M.O.R strategies.

1. R. – Read
2. U. – Underline Question
3. M. – Mark Information
4. O. – Operation
   • Write Equation
   • Build a model
   • Draw a picture
   • Make a list
   • Find a pattern
   • Work backwards
   • Guess and check
   • Others
5. R. – Recheck for Reasonableness

Now, Let’s look at the first math problem

Follow the strategies, we start from step 2 and we are asking to find the value of x.

From the problem, we know y=40, AB=BD, and AB is perpendicular to BC. And the most important information here is this problem is all about triangles.

Let's start to think about triangle and its properties:

1. What is the sum of interior angles of a triangle?
2. What is a isosceles triangle and its properties?
3. What is the value of an exterior angle?

Solution 1:

1. From AB is perpendicular to BC, we know ABC is a right angle.  So, angelABD + x = 90 and angleBAD + y = 90, right? Because y=40, angleBAD = 50.
2. From AB=BD, we know ABD is a isosceles triangle. So, angelBAD= angelBDA. Base on 1, we know angleABD = 180 - 2* angleBAD = 80. 
3. Then, from 1 and 2, x = 90 - angleABD = 10.

So, (A) is the right answer.

Solution 2:

Base on the Steps 1 and 2 in Solution 1, we know angleBDA = 50. The angleBDA is one of the exterior angles of triangle BDC which is the sum of angleDBC and angleDCB (this is y=40, right?). Then we have x + y = 50 and therefore x = 10.

Notes:

What we need to know about angles of a triangle?

1. The sum of interior angles is 180.
2. An measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
3. Isosceles Triangle Property :

• In a triangle, if two sides are equal, then the angles opposite the equal sides are also equal. (OR)
• In an isosceles triangle, the angles opposite the equal sides are equal.