Mathematics, 25.11.2019 21:31 sethjohnson386pbnm3x

△rst ~ △ryx by the sss similarity theorem. which ratio is also equal to rt/rx and rs/ry ?

a. xy/ts
b. sy/ry
c. rx/xt
d. st/yx

△rst ~ △ryx by the sss similarity theorem. which ratio is also equal to rt/rx and rs/ry ?

Answers: 3

Show answers

Answers

Answer from: cindy437596

Since, it is given that $\Delta RST \sim \Delta RYX$ by SSS similarity theorem.

We have to identify the ratio which is equal to $\frac{RT}{RX}$ and $\frac{RS}{RY}$ .

When the triangles are similar, then the ratio of the corresponding sides are always equal and the congruent angles are also equal.

Since, $\Delta RST \sim \Delta RYX$

So, $\frac{RT}{RX} = \frac{RS}{RY} = \frac{ST}{YX}$

So, the given ratios are equal to the ratio $\frac{ST}{YX}$ .

So, Option D is the correct answer.

Answer from: alexandroperez13

The triangle STX is similar to triangle YXR by the SSS similarity theorem. Option (A) is correct.

Further Explanation:

The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.

There are many similarity rules and are as follows.

1. Angle Angle Angle (AAA)

2. Side Side Side (SSS)

3. Side Angle Side (SAS)

Given:

The options are as follows.

(A). $\frac{{{\text{XY}}}}{{{\text{TS}}}}$

(B). $\frac{{{\text{SY}}}}{{{\text{RY}}}}$

(C). $\frac{{{\text{RX}}}}{{{\text{XT}}}}$

(D). $\frac{{{\text{ST}}}}{{{\text{YX}}}}$

Explanation:

The STX is similar to triangle YXR then the sides are proportional.

The proportional of corresponding side can be obtained as follows,

$\frac{{{\text{RT}}}}{{{\text{RX}}}}=\frac{{{\text{RS}}}}{{{\text{RY}}}}=\frac{{{\text{XY}}}}{{{\text{TS}}}}$ .

The corresponding sides are proportional. Therefore the triangles are similar.

The triangle STX is similar to triangle YXR by the SSS similarity theorem. Option (A) is correct.

Option (A) is correct as the ratio $\frac{{{\text{XY}}}}{{{\text{TS}}}}$ is equal to $\frac{{{\text{RT}}}}{{{\text{RX}}}}$ and $\frac{{{\text{RS}}}}{{{\text{RY}}}}$ .

Option (b) is not correct as the ratio $\frac{{{\text{SY}}}}{{{\text{RY}}}}$ is not equal to $\frac{{{\text{RT}}}}{{{\text{RX}}}}$ and $\frac{{{\text{RS}}}}{{{\text{RY}}}}$ .

Option (c) is not correct as the ratio $\frac{{{\text{RX}}}}{{{\text{XT}}}}$ is not equal to $\frac{{{\text{RT}}}}{{{\text{RX}}}}$ and $\frac{{{\text{RS}}}}{{{\text{RY}}}}$ .

Option (d) is not correct as the ratio $\frac{{{\text{ST}}}}{{{\text{YX}}}}$ is not equal to $\frac{{{\text{RT}}}}{{{\text{RX}}}}$ and $\frac{{{\text{RS}}}}{{{\text{RY}}}}$ .

Learn more:

1. Learn more about inverse of the function .

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle, similarity theorem.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

false

step-by-step explanation:

the reason i say this is because for a certain length of sides you can pick any two and the length is wither equal or greater than the third side and in this case it's not.

3 + 5 = 8

8 is smaller than 9 which is the third side.

hope this : )

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:00, ninaaforever

What is the area of mnp? 40 m2 60 m2 68 m2 127.5 m2

Answers: 2

continue

Mathematics, 21.06.2019 21:00, cicimarie2018

Choose the equation that represents the graph below: (1 point) graph of a line passing through points negative 3 comma 0 and 0 comma 3 y = x − 3 y = −x + 3 y = −x − 3 y = x + 3 will award !

Answers: 3

continue

Mathematics, 21.06.2019 22:20, macycj8

1. 2. ∠b and ∠y are right angles. 3.? 4.? which two statements are missing in steps 3 and 4? ∠x ≅ ∠c △abc ~ △zyx by the sas similarity theorem. ∠b ≅ ∠y △abc ~ △zyx by the sas similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem.

Answers: 2

continue

Mathematics, 21.06.2019 23:30, jacesmokesloud7254

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.

Answers: 3

continue

You know the right answer?

△rst ~ △ryx by the sss similarity theorem. which ratio is also equal to rt/rx and rs/ry ?