If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third
side.In triangle ABC , if D is midpoint of AB and DEllBC then find the ratio of AE : ED.
Answers
Answer:
Given:
In ΔABC, D is a midpoint of AB
DE // BC
To find:
1. The ratio of AE : ED
2. Draw the rough diagram of given data.
Solution:
(1). Finding the ratio of AE : ED :-
We know that,
: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
∴ ....... (i)
Since D is a midpoint of AB (given)
∴ AD = DB ...... (ii)
From (i) & (ii), we get
AE = EC
⇒ E is a midpoint of AC ..... (iii)
Now,
Consider Δ AED and ΔACB, we have
∠A = ∠A ........ [common angle]
∠ADE = ∠ABC ..... [corresponding angles, ∵DE//BC and side AB forms a transversal]
∴ Δ AED ~ ΔACB ........ By AA Similarity
Also, we know that the corresponding sides of two similar triangles are proportional to each other.
∴
on rearranging, we get
⇒
⇒
⇒
(2). Diagram of the given data:-
Rough diagram is attached below
---------------------------------------------------------------------------------------
Also View:
In the figure,DE ||BC If DB=6cm,AE=2cm,EC=4cm Find the length of AD
brainly.in/question/8960821
In figure.6.17. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii). (i) (ii)
brainly.in/question/1345137
In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ∆ADE and the trapezium BCED.
brainly.in/question/8027386
Read more on Brainly.in - https://brainly.in/question/17357087#readmore
hope its help you
mark as a brainliest
follow me
Answer:
Answer:
Given:
In ΔABC, D is a midpoint of AB
DE // BC
To find:
1. The ratio of AE : ED
2. Draw the rough diagram of given data.
Solution:
(1). Finding the ratio of AE : ED :-
We know that,
: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
∴ ....... (i)
Since D is a midpoint of AB (given)
∴ AD = DB ...... (ii)
From (i) & (ii), we get
AE = EC
⇒ E is a midpoint of AC ..... (iii)
Now,
Consider Δ AED and ΔACB, we have
∠A = ∠A ........ [common angle]
∠ADE = ∠ABC ..... [corresponding angles, ∵DE//BC and side AB forms a transversal]
∴ Δ AED ~ ΔACB ........ By AA Similarity
Also, we know that the corresponding sides of two similar triangles are proportional to each other.
∴
on rearranging, we get
⇒
⇒
⇒
(2). Diagram of the given data:-
Rough diagram is attached below
---------------------------------------------------------------------------------------