## Tuesday, September 27, 2011

### Geometry Part 2

Summary from Part 1

## 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 180Âº.

##### Proof:
Consider any triangle ABC in which the angles are aÂº, bÂº and cÂº.  Draw a line through A parallel to BC.

#### 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