jojo5998237
Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find y, ST and TU
Please help!

Find Y ST And TU Please Help class=

Sagot :

Given:

[tex]ST=4y,TU=2y+6[/tex]

To find:

The value of  y, ST and TU.

Solution:

In triangle STV and UTV,

[tex]m\angle TSV\cong n\angle TUV[/tex]            (Given right angles)

[tex]m\angle SVT\cong n\angle UVT[/tex]            (Given)

[tex]TV\cong TV[/tex]            (Common side)

The corresponding two angles and a non included sides in both triangles are congruent. So, the triangles are congruent by using AAS congruence postulate.

[tex]\Delta STV\cong \Delta UTV[/tex]           (AAS congruence postulate)

Corresponding parts of congruent triangles are congruent. So,

[tex]ST\cong UT[/tex]              (CPCTC)

[tex]4y=2y+6[/tex]

[tex]4y-2y=6[/tex]

[tex]2y=6[/tex]

[tex]y=3[/tex]

Now,

[tex]ST=4y[/tex]

[tex]ST=4(3)[/tex]

[tex]ST=12[/tex]

And,

[tex]TU=2y+6[/tex]

[tex]TU=2(3)+6[/tex]

[tex]TU=6+6[/tex]

[tex]TU=12[/tex]

Therefore, [tex]y=3,\ ST=12\ units,\ TU=12\ units[/tex].

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.