Answer:
PROPORTIONAL
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Step-by-step explanation:
Triangle Angle Bisector Theorem
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
By the Angle Bisector Theorem,
BDDC=ABAC
Proof:
Draw BE←→∥AD←→ .
Extend CA¯¯¯¯¯ to meet BE←→ at point E .
By the Side-Splitter Theorem,
CDDB=CAAE ---------( 1 )
The angles ∠4 and ∠1 are corresponding angles.
So, ∠4≅∠1 .
Since AD¯¯¯¯¯ is a angle bisector of the angle ∠CAB, ∠1≅∠2 .
By the Alternate Interior Angle Theorem , ∠2≅∠3 .
Therefore, by transitive property, ∠4≅∠3 .
Since the angles ∠3 and ∠4 are congruent , the triangle ΔABE is an isosceles triangle with AE=AB .
Replacing AE by AB in equation ( 1 ),
CDDB=CAAB
Example:
Find the value of x .
By Triangle-Angle-Bisector Theorem,
ABBC=ADDC .
Substitute.
512=3.5x
Cross multiply.
5x=42
Divide both sides by 5 .
5x5=425x=8.4
The value of x is 8.4 .
