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Standard X

Mathematics

Perpendicular from Right Angle to Hypotenuse Divides the Triangle into Two Similar Triangles

Consider the ...

Question

Consider the following statements:
i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.
ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.

(i) is correct and (ii) is false

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Both (i) and (ii) are false

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Both (i) and (ii) are correct

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(i) is false and (ii) is correct

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Solution

The correct option is A (i) is correct and (ii) is false
If the three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent by SSS rule.
if the three angles of one triangle are equal to three angles of another triangle, then the triangles are similar by AAA rule and not congruent.
Thus, (i) is correct, (ii) is false.

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Consider the following statements:i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.

Consider the following statements:
i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.
ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.