Question

Use the given information to prove that APQR ~ ARSP.GivenReflexive PropertyTransitive PropertyAddition and Subtraction PropertiesMultiplication and Division PropertiesSubstitution PropertyDefinition of Congruent SegmentsDefinition of MidpointDefinition of PerpendicularDefinition of Congruent Angles

Answer 1

Solution:

Given the figure;

Statement 1:

$\begin{gathered} \overline{PQ}\cong\overline{RS} \\ \end{gathered}$

Reason:

Given

Statement 2:

$\overline{QR}\cong\overline{SP}$

Reason:

Given

Statement 3:

$\begin{gathered} \overline{PR}\cong\overline{PR} \\ \end{gathered}$

Reason:

Reflexive property.

Statement 4:

$\triangle PQR\cong\triangle RSP$

Reason:

Side Side Side (SSS)