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

AA similarity postulate holds here.

Step-by-step 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

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

mental cunning

explanation:

he is often referred to as a man of twists and turns