Prove the triangle proportionality theorem.

Statement of triangle proportionality:  

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then that line divides these two sides proportionally.

From the statement: If then,

Show that:

Consider and

Reflexive property states that the value is equal to itself.

[Angle] {Reflexive property of equality}

Corresponding angles theorem states that if the two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent(i., e equal).

[Angle]

[Angle]

AA Similarity states that the two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

then, by AA similarity theorem:  

By segment addition postulates:

AB = FA +FB and AC = AG + GC  

Corresponding sides in similar triangles are proportional  

.....[1]

Substitute AB = FA +FB and AC = AG + GC in [1]  

we have;

Separate the fraction:

Simplify:

Subtract 1 from both sides we get;

hence proved

answer is 12345678900987654321234567890987654321

step-by-step explanation:

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step-by-step explanation:

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