Write a paragraph proof. Given: AD― and EC― intersect at B. Prove: △ABE∼△DBC

Step 1:To Prove Given: AD &amp; EC intersect at B To determine: △ABE∼△DBC Step 2:Proof In △ABE&amp;△DBC ABDB=124=3...(1) BEBC=155=3...(2) AEDC=10313=10103=3...(3) So, we have, ABDB=BEBC=AEDC So, by SSS congruence, △ABE∼△DBC Hence, Proved.

"Write a paragraph proof. Given: AD― and EC―..." solved and explained

High School
Geometry
High school geometry
Congruence

slaggingV

Answered question

2021-07-14

Write a paragraph proof.
Given:

\overset{―}{A D} and \overset{―}{E C}

intersect at B.
Prove:

△ A B E \sim △ D B C

Answer & Explanation

stuth1

Skilled2021-07-15Added 97 answers

Step 1:To Prove
Given:
AD & EC intersect at B
To determine:
$△ A B E \sim △ D B C$
Step 2:Proof
In $△ A B E & △ D B C$
$\frac{A B}{D B} = \frac{12}{4} = 3$ ...(1)
$\frac{B E}{B C} = \frac{15}{5} = 3$ ...(2)
$\frac{A E}{D C} = \frac{10}{3 \frac{1}{3}} = \frac{10}{\frac{10}{3}} = 3$ ...(3)
So, we have,
$\frac{A B}{D B} = \frac{B E}{B C} = \frac{A E}{D C}$
So, by SSS congruence,
$△ A B E \sim △ D B C$
Hence, Proved.

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