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------------------------------------------------ Is AABCDEF? If so, identify the similarity postulate or theorem that

applies.

A

B

16 105⁰

36

с

D

4

LLI

E

9

-105⁰

F

OA. Similar - AA

OB. Similar - SSS

OC. Similar - SAS

OD. Cannot be determined

4

C is the correct answer as both triangles have a similar angle of 105⁰ and both side lengths of triangle ABC are being divided by 4 to have the same two side lengths as triangle DEF

Answer Link

psm22415 psm22415 · Answer 2 · 2024-11-09T08:56:26-05:00

The triangles ΔABC and ΔDEF are similar triangles by SAS theorem

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔABC

The measure of side AB = 16

The measure of side AC = 36

And , the measure of ∠ABC = 105°

Let the first triangle be ΔDEF

The measure of side DE = 16

The measure of side DF = 36

And , the measure of ∠DEF = 105°

Now , the ratio of sides of the triangles is given by

AB / DE = AC / DF

4/16 = 9/36

1/4 = 1/4

So , corresponding sides of similar triangles are in the same ratio

And , the measure of angles = 105°

Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , they are similar triangles

To learn more about similar triangles click :

https://brainly.com/question/29378183

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