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Questions and Answers
For a pair of similar triangles, corresponding sides are always congruent.
For a pair of similar triangles, corresponding sides are always congruent.
False (B)
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
- NOT
- SAS (correct)
- SSS
- AA
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
- SAS
- NOT (correct)
- AA
- SSS
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Based on the given information, choose the similarity statement that you would use to say triangle ABC ~ triangle DEF.
Choose the next statement in the proof: Given: BC/CD = AC/CE, Prove: Triangle ACB is similar to Triangle ECD.
Choose the next statement in the proof: Given: BC/CD = AC/CE, Prove: Triangle ACB is similar to Triangle ECD.
Given: Angle A = Angle D, Prove: Triangle ACB ~ Triangle DCE.
Given: Angle A = Angle D, Prove: Triangle ACB ~ Triangle DCE.
Choose the next statement in the proof: Given: GF = 1/2 GC, GE = 1/2 GD, EF = 1/2 DC.
Choose the next statement in the proof: Given: GF = 1/2 GC, GE = 1/2 GD, EF = 1/2 DC.
Given: Segment YZ is parallel to Segment UV, Prove: XY/XU = YZ/UV.
Given: Segment YZ is parallel to Segment UV, Prove: XY/XU = YZ/UV.
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Study Notes
Similar Triangles and Their Properties
- Corresponding sides of similar triangles are not always congruent, indicating a difference in size while maintaining shape.
- For triangle similarity, Angle A equals Angle D leads to SAS (Side-Angle-Side) as the similarity statement.
Ratio and Proportionality
- The ratio BC/EF = 1/2 supports similarity through SSS (Side-Side-Side) relationship.
- When given BC = 6 and EF = 12, SAS similarity can be concluded from these proportional sides.
- If BC = 5 and EF = 15, it does not conclude similarity, indicating that proportionality alone is insufficient.
Proofs of Similarity
- Given BC/CD = AC/CE can lead to proving triangle ACB is similar to triangle ECD through angles and SAS.
- Vertical angles are equal, which supports the conclusion of similarity in triangle proofs.
Advanced Similarity Criteria
- For triangle GFE to be similar to triangle GCD, the proportions GF = 1/2 GC, GE = 1/2 GD, and EF = 1/2 DC establish SSS criteria and employ the Transitive Property of Equality.
- When segments YZ are parallel to segment UV, it implies XY/XU = YZ/UV due to the properties of similar triangles and equal alternate interior angles.
Conclusion
- Understanding the relationships between angles, sides, and the ratios is essential for determining triangle similarity.
- Proof statements rely on established geometric properties, including vertical angles and parallel line properties.
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