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Using Congruent Triangles

Learn how to deduce information about segments and angles after proving two triangles are congruent. Plan your proof effectively, use CPCTC, and popular reasons in a proof. Explore key properties and methods of congruence to complete proofs confidently.

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Using Congruent Triangles

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  1. Using Congruent Triangles Class Worksheet Part 2

  2. Helpful Information • Deducing information about segments and angles AFTER proving that the two triangles are congruent. • Sometimes it will be helpful to plan the proof before you get started. • Remember to start with the 3-2-3. • CPCTC always follows 2 congruent triangles. • Start at the ends and fill in the middle last.

  3. Popular Reasons in a Proof • Definition of a midpoint • Two Congruent Segments • Definition of a bisector (or angle bisector) • Two Congruent Segments (or angles) • Reflexive Property • Shared segments • Transitive Property • If a = b and b = c, then a = c. • Symmetric Property • If a = b, then b = a.

  4. More Popular Reasons… • Parallel Lines • Alternate Interior Angles • Corresponding Angles • Same Side Interior Angles • Vertical Angles • Methods of Congruence • SSS, SAS, ASA, AAS or HL

  5. Complete the following proof:

  6. Complete the following proof:

  7. Complete the following proof:

  8. Complete the following proof:

  9. Complete the following proof:

  10. Complete the following proof:

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