Given: $#\triangle QRS \text{ with } \overline {RS} \parallel \overleftrightarrow{XY}$#
Prove: $#{\large \frac {XQ}{RQ}} = {\large \frac {YQ}{RQ}}$#
Prove: $#{\large \frac {XQ}{RQ}} = {\large \frac {YQ}{RQ}}$#
Statement
Reason
1. $#\overleftrightarrow{RS} \parallel \overleftrightarrow{XY}$#
1. Given
2. $#\angle 1 \cong \angle 3, \angle 2 \cong \angle 4$#
2. If lines are || then corr. $#\angle$# s are $#\cong$#
3. $#\triangle QXY \sim \triangle QRS$#
3. AA $#\sim $# Postulate
4. $#{\large \frac {XQ}{RQ}} = {\large \frac {YQ}{RQ}} $#
4. Corr. sides of $#\sim \triangle$#s are proportional
5. $#XQ=XR+RQ$#,
$# YQ=YS+SQ $#
$# YQ=YS+SQ $#
5. Segment Addition Postulate
6. $#{\large \frac {XR+RQ}{RQ}} = {\large \frac {XS+SQ}{SQ}} $#
6. Substitute
7. $#{\large \frac {XR}{RQ}} + 1 = {\large \frac {XS}{SQ}}+1 $#
7. Simplification
8. $#{\large \frac {XQ}{RQ}} = {\large \frac {YQ}{RQ}} $#
8. Subtraction Property of =
9. QED
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