Tuesday, September 27, 2011

Geometry Part 2


 

Task 2

Your task is to steady the technique of solving the unknown/s stated in the questions below. Study the deduction and reasoning skills provided in the table.

(1) Given: m∠DGH = 131
      Find: m∠GHK
This argument is organized in two-column proof form below.
(2) Given: m∠1 = m∠3
      Prove: m∠PTR = m∠STQ
The two-column proof for this exercise is shown below.
(3) Given: m∠DCJ = 71, m∠GFJ = 46
      Prove: m∠AJH = 117
The two-column proof for this exercise is shown below.
(4) Given: m∠1 = 4x + 9, m∠2 = 7(x + 4)
      Find: m∠3
The two-column proof that shows this argument is shown below.

(5) Theorem 1: Prove that the angle sum of a triangle is 180º.

Proof:
Consider any triangle ABC in which the angles are aº, bº and cº.  Draw a line through A parallel to BC.


Task 3 

Complete the following:

1. Look at this diagram, write as many pairs as you can of

(a) vertically opposite

(b) corresponding

(c) alternate

(d) interior angles

2. Find the values of the pronumerals x and y in the following diagram.


sources:
http://www.wyzant.com
http://www.mathsteacher.com.au/year9/ch13_geometry/05_deductive/geometry.htm




Solution:
worksheet 2 solution

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