Triangle PQR ~ Triangle ABC and PQ:AB=2:5. If PM and AN are the medians, then find the ratio of their corresponding medians.
Answers
Answer:
If △ABC∼△PQR and
PQ
AB
=
5
7
then △ABC is bigger.
△ABC and △PQR are similar.
Therefore, their corresponding sides are proportional.
PQ
AB
=
QR
BC
=
RP
CA
=
5
7
⇒AB=
5
7
PQ,BC=
5
7
QR,CA=
5
7
RP
Here, sides of △ABC are
5
7
times that of the cooresponding sides of △PQR.
So , △ABC is bigger than △PQR.
Here, the correct answer is △ABC is bigger.
Concept: Similar figures mean once 2 figures square measure of constant form however square measure of various sizes. In alternative words, 2 figures square measure referred to as similar after they each have loads of constant properties however still might not be identical. For instance, the sun and moon may seem constant size however they're truly completely different in size. However, we tend to square measure similar figures since each the figures square measure circular in nature. This development is taken into account because the property of similarity keeping the form and distance in mind.
Given: ΔPQR~ ΔABC
PQ:AB=2:5
Find: Find the ratio of corresponding medians.
Solution: ΔPQR~ ΔABC
PQ:AB=2:5
Due to similarity, QR:BC=PQ:AB
Therefore, QR:BC=2:5
M and N are the intermediary of QR and BC respectively.
Therefore, their ratios are also equal that means PM:AN=QR:BC
= 2:5
Final answer: The ratio of medians are 2:5.
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