Question

find st and sv in parallelogram stuv.
st =
sv =
submit

Explanation:

Step1: Recall parallelogram side property

In a parallelogram, opposite sides are equal. So, \( TU = SV \) and \( ST = UV \). Wait, looking at the diagram, \( TU = c \) and \( SV = 2c - 48 \), so \( c = 2c - 48 \)? Wait no, maybe I misread. Wait, in parallelogram \( STUV \), \( ST \) and \( UV \) are opposite, \( SV \) and \( TU \) are opposite. Wait, the labels: \( T \) to \( S \) is \( 2c - 73 \), \( S \) to \( V \) is \( 2c - 48 \), \( U \) to \( T \) is \( c \), \( U \) to \( V \) should be equal to \( ST \), and \( SV \) equal to \( TU \). So \( SV = TU \), so \( 2c - 48 = c \).

Step2: Solve for c

\( 2c - 48 = c \)
Subtract \( c \) from both sides: \( 2c - c - 48 = 0 \)
\( c - 48 = 0 \)
Add 48 to both sides: \( c = 48 \)? Wait no, wait maybe \( ST = UV \) and \( SV = TU \). Wait, maybe I mixed up. Wait, \( ST \) is \( 2c - 73 \), \( UV \) should be equal to \( ST \). \( SV \) is \( 2c - 48 \), \( TU \) is \( c \), so \( SV = TU \), so \( 2c - 48 = c \). Wait, solving \( 2c - 48 = c \): \( 2c - c = 48 \), so \( c = 48 \). Then \( ST = 2c - 73 = 2*48 - 73 = 96 - 73 = 23 \). \( SV = 2c - 48 = 2*48 - 48 = 48 \)? Wait no, wait if \( SV = TU = c \), then \( 2c - 48 = c \), so \( c = 48 \), so \( SV = 48 \), \( ST = 2c - 73 = 2*48 -73 = 96 -73 =23 \). Wait, but let's check again. Wait, maybe the opposite sides: \( ST \) and \( UV \) are equal, \( SV \) and \( TU \) are equal. So \( ST = UV = 2c -73 \), \( SV = TU = c \). But also, maybe \( SV = 2c - 48 \), so \( c = 2c - 48 \), so \( c = 48 \). Then \( ST = 2*48 -73 = 23 \), \( SV = 48 \). Wait, but let's verify. If \( c = 48 \), then \( TU = 48 \), \( SV = 2*48 -48 = 48 \), so that's equal. \( ST = 2*48 -73 = 23 \), \( UV \) should be equal to \( ST \), so \( UV = 23 \). That works.

Wait, maybe I made a mistake in the property. Let's recall: In a parallelogram, opposite sides are congruent. So \( ST \cong UV \) and \( SV \cong TU \). So \( ST = UV \), \( SV = TU \). From the diagram, \( ST = 2c -73 \), \( TU = c \), \( SV = 2c -48 \), \( UV \) is not labeled, but \( SV \) and \( TU \) should be equal. So \( SV = TU \) implies \( 2c -48 = c \). Solving that: \( 2c - c = 48 \), so \( c = 48 \). Then \( ST = 2c -73 = 2*48 -73 = 96 -73 =23 \). \( SV = 2c -48 = 2*48 -48 = 48 \). Wait, but \( SV = TU = c = 48 \), which matches \( 2c -48 = 48 \) when \( c=48 \). So that works.

Answer:

\( ST = 23 \)
\( SV = 48 \)