Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Answer: :)
Step-by-step explanation:
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 ∠4and∠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 ∠3and∠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 .
The largest angle is 8.4.
what is Angle-Bisector theorem?
The Angle-Bisector theorem in geometry is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into. It compares their proportional lengths to the proportional lengths of the triangle's other two sides.
Given
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 ∠4and∠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 ∠3and∠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
5x/5=42/5=8.4
The value of x is 8.4 .
To learn more about the angle-bisector theorem refer to:
https://brainly.com/question/2478436
#SPJ2
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.