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zimovet [89]
3 years ago
5

Given scalene triangle DEF, explain how to find locus of points equidistant from DE EF DF using incenter

Mathematics
1 answer:
exis [7]3 years ago
5 0
Points equidistant from DE EF are in the bisector of angle DEF
points equidistant from EF DF are in the bisector of angle EFD
the sought after point is the intersection of bisectricess of triangle




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Line segment ST is dilated to create line segment S'T' using the dilation rule DQ,2. 25. Point Q is the center of dilation. Line
abruzzese [7]

The distance between points S' and S is x= 2.5 units.

<h2>Given that</h2>

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ 2. 25.

Point Q is the center of dilation.

Line segment ST is dilated to create line segment S prime T prime.

The length of QT is 1. 2 and the length of QS is 2.

The length of SS prime is x and the length of TT prime is 1. 5.

<h3>We have to determine</h3>

What is x, the distance between points S' and S?

<h3>According to the question</h3>

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ, 2.25.

Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5, SS' = x.

Since the line ST is dilated to S'T' with the center of dilation Q, the triangles STQ and S'T'Q must be similar.

We know that the corresponding sides of two similar triangles are proportional.

So, from ΔSTQ and ΔS'T'Q.

\dfrac{SQ}{S'Q} = \dfrac{TQ}{T'Q}\\&#10;\\&#10;\dfrac{SQ}{SQ+SS} = \dfrac{TQ}{TQ+TT'}\\&#10;\\ &#10;\dfrac{2}{2+x} = \dfrac{1.2}{1.2+1.5}\\\rm &#10;\\&#10;\dfrac{2}{2+x} = \dfrac{1.2}{2.7}\\\\ \dfrac{2}{2+x} = \dfrac{12}{27}\\\\2(27) = (2+x) 12\\\\ 54 = 24 + 12x\\&#10;\\&#10;12x = 54-24\\&#10;\\&#10;12x=30\\&#10;\\&#10;x = \dfrac{30}{12}\\&#10;\\&#10;x = 2.5

Hence, the distance between points S' and S is x= 2.5 units.

To know more about Pythagoras Theorem click the link given below.

brainly.com/question/16016926

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3 years ago
I) Consider the following figure,<br><br> ​<br><br> ​<br><br> ​
qwelly [4]

Step-by-step explanation:

If PQRS is a quadrilateral inscribed in a circle, then the opposite angles of the quadrilateral are <u>supplementary</u><u>.</u>

y + 68° = 180° { being opposite angles of cyclic quadrilateral }

y = 180° - 68°

y = 112°

x + 82° = 180° { being opposite angles of cyclic quadrilateral }

x = 180° - 82°

x = 98°

Hope it will help :)❤

4 0
2 years ago
Estimate the measure of 1.
ivann1987 [24]

Answer:

about 80º give or take

Step-by-step explanation:

it's not quite 90 degrees, and its not 70 degrees or below.

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How many students were surveyed?<br>​
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Step-by-step explanation:

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Anyone would like to do this im so bad at math lm(a)o you will get brainliest if you do this correctly
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