Q3 of 70 Page 140

Can two similar triangles have same area? If yes, in which case they have the same area?

Yes, two similar triangles can have same area.

Note, when two triangles are congruent then all corresponding sides as well as corresponding angles of one triangle are equal to those of the other triangle.


⇒ If two triangles are congruent, they are similar too.


And congruent triangles have same area too.


Hence, the similar triangles need to be congruent to have similar areas.


More from this chapter

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1

In ΔABC, such that are positive real numbers. A line passing through P and parallel to intersects in Q. Prove that (m + n)2 (area of ΔAPB) = m2(area of ΔABC)

 2

D, E and F are the mid-points of, and respectively in ΔABC. Prove that the area of □ BDEF = 1/2 area of ΔABC.

 4

The correspondence ABC ↔ DEF is similarity in ΔABC and ΔDEF. is an altitude of ΔABC and is an altitude of ΔDEF. Prove that AB X DN = AM X DE.

 5

Explain with reasons, whether the following statements are true or false:

(1) AAA criterion of similarity of triangles cannot be the criterion for congruence of triangles.


(2) SAS criterion for congruence of triangles cannot be a criterion for similarity of triangles.


(3) Two congruent triangles have the same area.


(4) Two similar triangles always have the same area.


(5) Area of similar triangles are proportional to the squares of measures of their corresponding angles.