Math / Geometry

QuestionWhat values of $v$ and $w$ make $\triangle B C D \cong \triangle T U S$ ? $\begin{aligned} v & =\square \\ w & =\square \end{aligned}$ Submit

Studdy Solution

STEP 1

1. The triangles $\triangle BCD$ and $\triangle TUS$ are right triangles.
2. The triangles are congruent by the criteria that their corresponding sides are equal.
3. The corresponding sides of the triangles are $BC$ with $TU$ , $BD$ with $US$ , and $CD$ with $UT$ .

STEP 2

1. Set up equations for the corresponding sides.
2. Solve the equations for $v$ and $w$ .

STEP 3

Set up equations for the corresponding sides:
1. $BC = TU$ $ 20w - 4 = 18w \]
2. $BD = US$ $ 5v + 1 = 2v + 49 \]

STEP 4

Solve the equations for $v$ and $w$ .
1. Solve for $w$ from the equation $20w - 4 = 18w$ :
20w - 18w = 4 \] 2w = 4 \] $ w = 2 \]
2. Solve for $v$ from the equation $5v + 1 = 2v + 49$ :
5v - 2v = 49 - 1 \] 3v = 48 \] $ v = 16 \]
The values that make $\triangle BCD \cong \triangle TUS$ are:
$v = 16$ $w = 2$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms