Maths Class 10th question
1) Write the statement of basic proportionality theorem and prove it with diagram.
Answers
Answer:
HI
Step-by-step explanation:
filledbookmark
USE APP
Sign in
Questions & Answers
CBSE
Mathematics
Grade 10
Basic Proportionality Theorem or Th...
Question
Answers
Free Download
Related Questions
State BPT theorem and prove it.
Answer
VerifiedVerified
59.6k+ views
7.6k+ likes
Hint: To prove this theorem first we will join BE and CD. Then draw a line EL perpendicular to AB and line DM perpendicular to AC. Now we will find the ratio of area of Δ
ADE to Δ
DBE and ratio of area of Δ
ADE to Δ
ECD. Comparing the ratios we will get the final answer.
Complete step-by-step answer:
Now, ΔDBE
and ΔECD
being on the same base DE and between the same parallels DE and BC, we have,ar(ΔDBE)=ar(ΔECD)
then we say that the basic proportionality theorem is proved.
Basic proportionality theorem:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
Given:
A ΔABC
in which DE∥BC
and DE intersects AB and AC at D and E respectively.
To prove that:
ADDB=AEEC
Construction:
Join BE and CD.
Draw EL⊥AB
and DM⊥AC
Proof:
We have the
ar(ΔADE)=12×AD×EL
ar(ΔDBE)=12×DB×EL
Therefore the ratio of these two is ar(ΔADE)ar(ΔDBE)=ADDB
. . . . . . . . . . . . . . (1)
Similarly,
ar(ΔADE)=ar(ΔADE)=12×AE×DM
ar(ΔECD)=12×EC×DM
Therefore the ratio of these two is ar(ΔADE)ar(ΔECD)=AEEC
. . . . . . . . . . . .. . . (2)
Now, ΔDBE
and ΔECD
being on the same base DE and between the same parallels DE and BC, we have,
ar(ΔDBE)=ar(ΔECD)
. . . . . . . . . . . (3)
From equations 1, 2, 3 we can conclude that
ADDB=AEEC
Hence we can say that the basic proportionality theorem is proved.
Note: The formula for area of the triangle is given by 12×b×h
where b, h are base and height respectively. If two triangles are on the same base and between the same parallels then the area of those two triangles are equal.
HOPE IT HELPS YOU
PLZ MARK ME BRAINLIST
