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Understanding Congruent Triangles: Properties and Examples

In this lesson, we explore the concept of congruence in triangles, focusing on properties such as corresponding angles and sides. Using Vito Acconci's geometric furniture design, we analyze angles FCB and CFE, and determine the similarity and congruence of triangles ABC and DEF. We also delve into essential theorems like the Third Angles Theorem and properties of congruent triangles, including reflexive, symmetric, and transitive properties. Engage with examples and practice exercises to reinforce learning on this crucial geometric topic.

sebastian-lane
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Understanding Congruent Triangles: Properties and Examples

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  1. Congruent Triangles – Day 2 Congruence & Triangles

  2. Warm-Up - Artists • Vito Acconci is a popular American sculptor and artist. One of his furniture creations called the Name Calling Chair uses a variety of geometric shapes, such as squares and triangles. The back of the chair is shown in the diagram. • What do you know about angles FCB and CFE? • Are triangles ABC and DEFsimilar? • Are triangles ABC and DEFcongruent?

  3. Congruent Figures • Exact same shape • Exact same size Congruent Not Congruent

  4. Properties of Congruent Figures • Corresponding Angles are Congruent • Corresponding Sides are congruent B Q R C A P Corresponding angles: <A & <P, <B & <Q, <C & <R Corresponding Sides: AB & PQ, BC & QR, AC & PR

  5. Example 1: Write a congruence statement and identify all corresponding parts. H Y K X Z J

  6. Example 2: ABCD KJHL B K (4x – 3) cm 9 cm 6 cm J D (2y – 4)o H A 91 86 L C Find the value of x Find the value of y

  7. Third Angles Theorem • If 2 angles in a triangle are congruent to 2 angles in a 2nd triangle, then the 3rd angles are also congruent. E B D F A C

  8. Example 3: Find the value of x F (4x+15)o E B D 87o 22o A C

  9. Example 4: Decide whether the triangles are congruent. Justify reasoning. H E 58o G 58o F J

  10. Homework – Day 2 • Pg. 206 #10 – 21, 24, 26, 28

  11. Theorem 4.4 Properties of Congruent Triangles • Reflexive Property • Every triangle is congruent to itself • Symmetric Property • If ABC = DEF, then DEF = ABC • Transitive Property • If ABC = DEF and DEF = JKL, then ABC = JKL

  12. 4.1/4.2 Practice

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