# To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that

###### Question:

## Answers

The two triangles are congruent it two sides and the included angle of one triangle are respectively equal to two sides and angle of the other triangle

A c=c

Step-by-step explanation:

C

Step-by-step explanation: I worked it out for you :)

AC/GI=BC/H

Step-by-step explanation:

we know that

The Side-Angle-Side Similarity Theorem states that: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem the included angle is

∠C≅∠I

therefore

side AC must be proportional to side GI and side BC must be proportional to side HI

so

AC/GI=BC/HI

Verify

substitute the given values

15/9=20/12

15*12=20*9

180=180 > is true

therefore

The two sides are proportional

answer:

it needs to be shown that

one pair of sides that are congruent

one pair of angles that are congruent

another pair of sides that are congruent

Both are similar by SAS similarity.

This SAS similarity is equivalent to the congruence.

Step-by-step explanation:

Step 1:

To prove that ACB and HIG as similar triangles.

We have to look upon the corresponding sides.

SAS= Side angle sides , there the angle must be in between two sides.

[tex]\angle[/tex] ACB = [tex]\angle[/tex] HIG

Lets work on the corresponding sides.

IG/AC = IH/AC

[tex]\frac{9}{15}[/tex] = [tex]\frac{12}{20}[/tex]

Reducing each to lowest form, we divide numerator and denominator by 3 for the 1st fraction and by 4 for the 2nd fraction.

We have

[tex]\frac{3}{5}[/tex] = [tex]\frac{3}{5}[/tex]

Both sides are equal.

So its proved that both are similar with SAS similarity theorem.

[tex]Consider the two triangles. triangles a b c and h g i are shown. angles a c b and h i g are right an[/tex]

D

Step-by-step explanation:

i took the test on edg bruh good luck

do youu have some image? because I take a test about that

Step-by-step explanation:

For this case, we have that by definition, the triangle similarity theorem related to the angles, establishes that:

For two triangles to be similar, the angles of one of them must be congruent to the angles of the other triangle.On the other hand, we have:

For a pair of triangles to be similar, it is sufficient to have a congruent angle between the proportional sides.In addition, we have the following side theorem (SSS):

Two triangles that have the three proportional sides are similar to each other.ANswer:

Two triangles that have the three proportional sides are similar to each other.

The triangle has two sides that are equivalent and the angle where the two meet are also equivalent.

In other words, two sides and the angle between them are congruent.

Hope this helps, if it does please give me brainliest, it will help me a lot :)

Have a good day