Question

Statement I: Two triangles are similar if two corresponding angles are equal.
Statement II: The sum of internal angles in a triangle is ${180}^{\circ }$.

• A. Statement I is true. Statement II is true. Statement II is the correct explanation of Statement I.
• B. Statement I is true. Statement II is true. Statement II is not the correct explanation of Statement1.
• C. Statement I is true. Statement II is false.
• D. Statement I is false. Statement II is true.

Answer 1

The correct option is A Statement I is true. Statement II is true. Statement II is the correct explanation of Statement I.

Consider two triangles, $\Delta$ ABC and $\Delta$ DEF in which
$\angle A$$=\angle D,\angle B=\angle E$.
We know that sum of internal angles in a triangle is 180${}^{\circ }$.
The third angle can be obtained by
$\angle C={180}^{\circ }-\angle A-\angle B$.
Similarly the third angle in $\Delta$ DEF is
$\angle F={180}^{\circ }-\angle D-\angle E={180}^{\circ }-\angle A-\angle B=\angle C.$
Hence the three angles are equal and by AAA similarity the two triangles are similar.