Question

Which theorem or postulate proves that △ABC and △DEF are similar?

Drag and drop the correct postulate or theorem into the box to correctly complete the statement.

The two triangles are similar by the

AA similarity postulate
SAS Similarity Theorem
SSS Similarity Theorem

Answer 1

For similarity measures of corresponding angles should be equal so we would use AA similarity postulate

Answer 2

AA similarity postulate holds here.

Explanation:

As in right angled ΔCAB and ΔFDE we are given two angles each and with the help of property that in a triangle the sum of all the angles of a triangle is equal to 180° w can find out the measure of third angle.

In ΔCAB we have:

∠A=90° and ∠B=37°.

The measure of third angle i.e. ∠C will be:

∠A+∠B+∠C=180°

90°+37°+∠C=180°

∠C=180°-127°

⇒ m∠C=53°

Similarly in ΔFDE we get:

m∠E=37° ( since we are given ∠F=53° and ∠D=90°)

Hence clearly all the corresponding angles in both the triangles are equal.

Hence AAA similarity holds.

Hence, both the triangles are similar.

Hence, first option is true.

AA similarity postulate