Question

If RT bisects SU, find each measure ST, RU, SV, SU,

Answer 1

Answer:

ST = 23

RU = 8

SV = 5

SV = 10

Step-by-step explanation:

Use the knowledge of the properties of a kite to find the measure of ST, RU, SV, and SU as shown below:

✍️Recall: Each pair of adjacent sides of a kite are congruent/equal.

ST and TU are a pair of adjacent sides.

TU = 23

✅Therefore, ST = 23.

RU and RS are a pair of adjacent sides.

RS = 8

✅Therefore, RU = 8.

✍️ Recall: the longer diagonal of a kite bisects the shorter one. This means RT divides SU into two equal parts, namely SV and UV.

Since UV = 5, therefore,

✅SV = 5

SU = UV + SV

✅SV = 5 + 5 = 10

Answer 2

A bisector divides the lines it bisects into equal segments

The measures of ST, RU, SV, SU are 23, 8, 10 and 5 respectively

From the diagram, we have:

$\mathbf{TU = 23}$

$\mathbf{UV = 5}$

$\mathbf{RS = 8}$

Because RT bisects SU, then:

$\mathbf{ST = TU}$

So, we have:

$\mathbf{ST = 23}$

Also, we have:

$\mathbf{RU = RS}$

So, we have:

$\mathbf{RU = 8}$

Also, we have:

$\mathbf{SV =VU \times 2}$

$\mathbf{SV =5 \times 2}$

$\mathbf{SV =10}$

Lastly, we have:

$\mathbf{SU =VU}$

$\mathbf{SU =5}$

Hence, the measures of ST, RU, SV, SU are 23, 8, 10 and 5 respectively

Read more about bisectors at:

https://brainly.com/question/13438893