Triangle Congruence Unit Review

Which pair of triangles can be proven congruent by the HL theorem?

What is the missing reason in the proof that ΔRST ≅ ΔVST?

Which rigid transformation would map ΔABC to ΔEDC?

Which single rigid transformation is required to map ΔDEF onto ΔD'EF'?

Which pair of triangles can be proven congruent by SAS?

How can ΔABC be mapped to ΔXYZ? First, translate ______________.

Which rigid transformation would map ΔABC to ΔABF?

To prove that triangles FHG and KJG are congruent by ASA, which statement and reason could be used as part of the proof?

Is ΔWXZ ≅ ΔYZX? Why or why not?

Could ΔABC be congruent to ΔADC by SSS? Explain.

What are the rigid transformations that will map ΔABC to ΔDEF?

Which statement and reason would be included in Roberto's proof that was not included in Nessa's proof?

Triangle Congruence Theorems

HL (Hypotenuse-Leg) theorem can prove congruence for right triangles with matching hypotenuse and one leg.
SAS (Side-Angle-Side) theorem proves congruence with two sides and the included angle matching.
SSS (Side-Side-Side) theorem establishes congruence by comparing all three corresponding sides.

Rigid Transformations

Rigid transformations include translations, rotations, and reflections, which maintain shape and size during movement.
Specific transformations can map one triangle onto another, indicating congruence.
Triangle mapping examples illustrate how to align triangles through a combination of transformations.

Triangle Proofs

Proofs often involve given conditions, such as parallel lines or congruent sides to validate triangle congruence.
ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) can also establish triangle congruence effectively.
Additional statements in proof formulations can help establish relationships not covered in previous arguments.

Compatibility of Triangles

Determining congruence involves assessing matching sides and angles carefully.
Situations where triangles cannot be congruent must be explained clearly, focusing on the discrepancies in side or angle measures.

Practical Applications

Consider each theorem and transformation when exploring triangle relationships in geometric problems.
Familiarity with proof structures enhances one’s ability to demonstrate congruence logically and effectively.

Test your understanding of triangle congruence with this review quiz. Covering the HL theorem, proofs, and rigid transformations, you'll strengthen your grasp on important geometric concepts. Perfect for students preparing for exams on this topic.