MHB Need help with parallelogram proof

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SUMMARY

The discussion focuses on proving the relationship between the segments in a parallelogram, specifically using similar triangles WYS and STW. The user establishes that opposite sides and angles of the parallelogram WYST are congruent, which allows for the application of the Side-Angle-Side (SAS) similarity criterion. The key conclusion is that the segments SX x YW must equal SV x WT, based on the properties of similar triangles and the congruence of opposite sides in parallelograms.

PREREQUISITES
  • Understanding of parallelogram properties, including congruent sides and angles.
  • Knowledge of triangle similarity criteria, particularly Side-Angle-Side (SAS).
  • Familiarity with geometric proofs and reasoning.
  • Ability to analyze and compare proportions in similar triangles.
NEXT STEPS
  • Study the properties of parallelograms in depth, focusing on congruence and similarity.
  • Learn about the various triangle similarity criteria, including SAS, SSS, and AA.
  • Practice geometric proofs involving parallelograms and similar triangles.
  • Explore applications of similar triangles in solving real-world problems.
USEFUL FOR

Students learning geometry, educators teaching geometric proofs, and anyone seeking to understand the properties of parallelograms and triangle similarity.

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Hello, we are learning about similar triangles and this was a problem. So I know that opposite sides of a parallelogram are congruent as are opposite angles, so I can establish similarity with triangles WYS and STW, but I don't understand how that proves SX x YW = SV x WT because the proportions don't match up when I compare similar triangles for their corresponding parts.

Any help is greatly appreciated... am I on the right track?

This is what I have so far. See attached image.

Statement Reason

1. WYST is Parallelogram. 1. Given
2. angle Y and angle T are congruent. 2. Def of parallelogram, opposite angles congruent.
3. WT and YS congruent, WY and TS congruent. 3. Def of parallelogram, opposite sides congruent.
4. WYS and STW are similar. 4. SAS
?
 

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The similar triangles that you need to look at are $SXY$ and $SVT$. Then use the fact that opposite sides of the parallelogram are equal.
 

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