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In right Delta RQT,overline (QS) is a median Complete. 1. If ST=8 , then QS= square 2. If QS=12 , then RT = RT=square 3. If mangle T=55 , then mangle SQT=square 4. If mangle T=65 , then mangle RQS=square

Pergunta

In right Delta RQT,overline (QS) is a median Complete.
1. If ST=8 , then QS= square 
2. If QS=12 , then RT =
RT=square 
3. If mangle T=55 , then
mangle SQT=square 
4. If mangle T=65 , then
mangle RQS=square

In right Delta RQT,overline (QS) is a median Complete. 1. If ST=8 , then QS= square 2. If QS=12 , then RT = RT=square 3. If mangle T=55 , then mangle SQT=square 4. If mangle T=65 , then mangle RQS=square

Solução

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MargaridaVeterano · Tutor por 9 anos

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To solve these problems, we need to understand the properties of a median in a right triangle and how angles relate to each other.<br /><br />1. If \( S T=8 \), then \( Q S= \) \( 8 \).<br /><br /> Since \( \overline{Q S} \) is a median, it divides the hypotenuse \( \overline{R T} \) into two equal segments. Therefore, if \( S T = 8 \), then \( Q S = 8 \).<br /><br />2. If \( Q S=12 \), then \( R T= \) \( 24 \).<br /><br /> Again, since \( \overline{Q S} \) is a median, it divides the hypotenuse \( \overline{R T} \) into two equal parts. Thus, if \( Q S = 12 \), then the full length of the hypotenuse \( R T = 2 \times 12 = 24 \).<br /><br />3. If \( m \angle T=55 \), then \( m \angle S Q T= \) \( 35 \).<br /><br /> In a right triangle, the sum of the angles is always \( 180^\circ \). Given that one angle is \( 90^\circ \) (the right angle), the other two angles must add up to \( 90^\circ \). Therefore, if \( m \angle T = 55^\circ \), then \( m \angle S Q T = 90^\circ - 55^\circ = 35^\circ \).<br /><br />4. If \( m \angle T=65 \), then \( m \angle R Q S= \) \( 25 \).<br /><br /> Similarly, using the same reasoning as above, if \( m \angle T = 65^\circ \), then \( m \angle R Q S = 90^\circ - 65^\circ = 25^\circ \).
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