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Congruent Triangles – Day 2

Congruent Triangles – Day 2. Congruence & Triangles. Warm-Up - Artists.

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Congruent Triangles – Day 2

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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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