Mathematics, 04.02.2020 14:55 alexkoval1231

What information is necessary to prove two triangles are similar by the sas similarity theorem?

Answers: 2

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Answers

SAS similarity theorem says that the two sides of one triangle are proportional to the other sides of the another triangle an one included corresponding angles are congruent.

Further explanation:

SAS similarity theorem says that the two sides of one triangle are proportional to the other sides of the another triangle an one included corresponding angles are congruent.

It can be better explained through an example.

Step 1:

Consider the two triangles $\Delta OMN{\text{ and }}\Delta SQR$ that the corresponding sides are written below.

$\begin{aligned}ON \to SR \hfill\\OM \to QS \hfill \\MN \to QR \hfill\\\end{aligned}$

Step 2:

The length of is 8 units and the length of is 32 units.

Therefore, the ratio of and can be expressed as,

$\begin{aligned}\frac{{SR}}{{ON}} &= \frac{{32}}{8}\\\frac{{SR}}{{ON}} &= 4\\\end{aligned}$

Step 3:

The length of is 15 units and the length of is 60 units.

Therefore, the ratio of and can be expressed as,

$\begin{aligned}\frac{{SQ}}{{OM}} &= \frac{{60}}{{15}}\\\frac{{SQ}}{{OM}} &= 4\\\end{aligned}$

Step 4:

In the triangle ${\text{ }}\Delta SQR$ the angle $\angle QSR = 60^\circ$ .and in $\Delta OMN$ the angle $\angle NOM = 60^\circ$ .

These two angles $\angle QSR = 60^\circ$ and $\angle NOM = 60^\circ$ are corresponding congruent angles.

Step 5:

It can be seen that the ratio of corresponding sides of the triangle are proportionalas,

$\dfrac{{SR}}{{ON}} = \frac{{SQ}}{{OM}} = 4$

Therefore, it satisfies the condition of SAS similarity theorem.

Thus, $\Delta OMN{\text{ and }}\Delta SQR$ are similar by SAS theorem.

Learn more:

Learn more about SSS similarity theorem Learn more about the symmetry for a function Learn more about midpoint of the segment

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Triangle similarity.

Keywords: Triangle, similarity, sides, proportional, ratio, length, theorem, diagram, corresponding sides, angles, sum, fraction

Answer from: Quest

step-by-step explanation:

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5856

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5458

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565

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8/95

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(80 points for all these questions) if you could for all these and you

Answer from: Quest

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

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