Geometri for School

GEOMETRI FOR SCHOOL

PROPORTIONAL SEGMENTSBY:

ANDI AMIRAH MU’MINATI1311441027

Proportional SegmentsIf the two segments are

divided proportionately,

(1)The corresponding new

segments are in

proportion, and

(2)The two original

segments and either pair

corresponding new

segments are in

proportion.

7.3A Obtaining the Eight Arrangements of any problems

A proportion such us can be arranged in eight ways. To obtain the eight variations, we let each term of the proportion respect one of the new segments. Two of the possible proportions are then obtained from each direction, as follows:

7.3 B Principles of the proportion Segments

Principle 1: If a line is parallel to one side of a triangle,

then it divides the other two sides proportionately.

Principle 2: If a line divides two sides of a triangle

proportionately, it is parallel to the third side.

Principle 3Three or more parallel lines divided any two

transversals proportionately.

Thus in Fig. 7-3, then =.

Principle 4: A bisector of an angle of triangle divides the opposite side

into segments which are proportional to the adjacent sides.Thus in of Fig. 7-4, if bisect then =.

Applying Principle I and 2

• Find x in each part of Fig.7-5

Applying Principle 3

• Find x in each part of Fig.7-6

Applying Principle 4

• Find x in each part of Fig.7-7

Proving a Proportional Segments Problem

• Given: • To Prove: • Plan: Prove that divides

and proportionately.

Statements Reasons1. 1.Given

2. 2. A line (segments) parallel to one side of a triangle

3. 3. Substitution Postulate

4. 4. If a line divides two sides of triangle proportionately, it is parallel to the third side

Daftar Pustaka:Schaum's Outline of Geometry