Sunday 18 August 2013

Day 5 Blog - Geometry

We were reminded of the different names of triangles such as Scalene, Isosceles and Equilateral triangles in this lesson. When Dr Yeap gave us the first problem: "Show 2 ways of showing 60 degree angle". It took me awhile to verify the ways  as i took it for granted that 3 angles of a triangle is 180 degree and each angle is 60 degree. When he questioned "How would you know is 60 degree", i couldn't answer thinking aloud "Isn't it known that each angle in a triangle is 60 degree??"
I like the idea of folding the triangle down so that all angles are in a straight line to be useful.

Today the main problem is:



This problem is tough for me handle. As what Dr Yeap mentioned, I lacked the "visualisation" that allows me to spot angle ADC and CEF to be 162 degrees too. It is a good recap for me to challenge myself!


Types of angles

Acute angle:

An angle whose measure is less than 90 degrees. The following is an acute angle.

Acute-angle-image

Right angle:

An angle whose measure is 90 degrees. The following is a right angle.

Right-angle-image

Obtuse angle:

An angle whose measure is bigger than 90 degrees but less than 180 degrees. Thus, it is between 90 degrees and 180 degrees. The following is an obtuse angle.

Obtuse-angle-image

Straight angle

An angle whose measure is 180 degrees.Thus, a straight angle look like a straight line. The following is a straight angle.

Straight-angle-image

Reflex angle:

An angle whose measure is bigger than 180 degrees but less than 360 degrees.The following is a reflex angle.Reflex-angle-image

Adjacent angles:

Angle with a common vertex and one common side. <1 and <2, are adjacent angles. Adjacent-angle-image

Complementary angles:

Two angles whose measures add to 90 degrees. Angle 1 and angle 2 are complementary angles because together they form a right angle.

Note that angle 1 and angle 2 do not have to be adjacent to be complementary as long as they add up to 90 degrees

complemenetary-angle-image

Supplementary angles:

Two angles whose measures add to 180 degrees. The following are supplementary angles.

Supplementary-angle-image

Vertical angles:

Angles that have a common vertex and whose sides are formed by the same lines. The following(angle 1 and angle 2) are vertical angles.

Verical-angle-image

When two parallel lines are crossed by a third line(Transversal), 8 angles are formed. Take a look at the following figure

Transverlines-image

Angles 3,4,5,8 are interior angles

Angles 1,2,6,7 are exterior angles

Alternate interior angles:

Pairs of interior angles on opposite sides of the transversal.

For instance, angle 3 and angle 5 are alternate interior angles. Angle 4 and angle 8 are also alternate interior angles.

Alternate exterior angles:

Pairs of exterior angles on opposite sides of the transversal.

Angle 2 and angle 7 are alternate exterior angles.

Corresponding angles:

Pairs of angles that are in similar positions.

Angle 3 and angle 2 are corresponding angles.

Angle 5 and angle 7 are corresponding angles

No comments:

Post a Comment