Fill in the blanks with similar/not similar
(ii) All equilateral triangles are______

Open in App

Solution

Let us assume two triangles $△ P Q R$ and $△ X Y Z$
In $△ P Q R$
$P Q = Q R = P R$ i.e. all sides are equal.
So, $△ P Q R$ is equilateral
Similarly, $△ X Y Z$ is equilateral as $X Y = X A = Y Z$
Now,
$\frac{X Y}{P Q} = 2$
$\frac{X Z}{P R} = 2$
$\frac{Y Z}{Q R} = 2$
So,
$\frac{X Y}{P Q} = \frac{X Z}{P R} = \frac{Y Z}{Q R}$
So, sides are in same ratio
Hence, equilateral triangles are similar.

Suggest Corrections

Similar questions

Fill in the blanks using correct word given in the brackets:−

(i) All circles are __________. (congruent, similar)

(ii) All squares are __________. (similar, congruent)

(iii) All __________ triangles are similar. (isosceles, equilateral)

(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are __________ and (b) their corresponding sides are __________. (equal, proportional)

Q. Fill in the blanks using the correct word in the given bracket.
(iii) All

___

triangles are similar. (isosceles, equilateral).

Q. Fill in the blanks with similar /not similar
(iii) All isosceles triangles are________

Q. Question 1 (iii)
Fill in the blanks using the correct word in the given bracket.

(iii) All____triangles are similar. (isosceles, equilateral)

Question 1 (iii)
Fill in the blanks using the correct word in the given bracket.

(iii) All ___ triangles are similar. (isosceles, equilateral)

Join BYJU'S Learning Program

Fill in the blanks with similar/not similar(ii) All equilateral triangles are______

Let us assume two triangles △PQR and △XYZ In △PQRPQ=QR=PR i.e. all sides are equal.So,△PQR is equilateral Similarly, △XYZ is equilateral as XY=XA=YZNow, XYPQ=2XZPR=2YZQR=2So,XYPQ=XZPR=YZQRSo, sides are in same ratioHence, equilateral triangles are similar.

Fill in the blanks with similar/not similar
(ii) All equilateral triangles are______