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NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ Lesson 14 M1 Period:________ Date:__________ GEOMETRY Lesson 14: Congruent Figures - Triangles Learning Target: I can list pairs of corresponding angles and sides on congruent triangles Things that we should know …… The word "congruent" is defined in the dictionary as “identical” in form Congruent figures are the same size and shape. It is possible to turn, flip and/or slide one figure so it will fit exactly on the other figure. The areas of congruent figures are equal. The perimeters of congruent figures are equal. The corresponding angles of congruent figures are equal in measure. The corresponding line segments of congruent figures are equal in length These triangles are ≅ These two figures are not ≅ For congruent (≅) triangles, all the angles are congruent AND all the corresponding sides are congruent. Naming Congruent Triangles The naming of congruent triangles is important: order matters. The statement: ΔABC is congruent to ΔDEF indicates that these triangles are congruent. Therefor all corresponding angles and sides are congruent Angle measures are equal: 𝑚∠𝐴 = 𝑚∠𝐷 𝑚∠𝐵 = 𝑚∠𝐸 𝑚∠𝐶 = 𝑚∠𝐹 Lengths are equal: 𝐴𝐵 = 𝐷𝐸 𝐵𝐶 = 𝐸𝐹 𝐶𝐴 = 𝐹𝐷 Draw the triangles NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ Lesson 14 Period:________ Date:__________ Identifying Corresponding Parts Example 1. Given that 𝛥𝐴𝐵𝐶 is congruent to 𝛥𝐷𝐸𝐹, identify all the congruent corresponding parts a. three pairs of congruent sides b. three pairs of congruent angles c. Given that 𝛥𝐴𝐵𝐶 is congruent to 𝛥𝐷𝐸𝐹, mark these triangles accordingly. Example 2 Example 3 Given that 𝛥𝐴𝐵𝐶 ≅ 𝛥𝐿𝑀𝑁, identify all the corresponding angles and sides. Corresponding Sides Corresponding Angles Draw a diagram M1 GEOMETRY NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 Name:__________________________________ M1 GEOMETRY Period:________ Date:__________ Lesson 14: Congruent Figures - Triangles Classwork 1. Given that ABC XYZ, identify and mark all of the congruent corresponding parts in the diagram. 2. CAT JSD. List each of the following. a. three pairs of congruent sides b. three pairs of congruent angles For exercises 3 – 5 list the corresponding sides and angles. 3. Pairs of ≅ angles (#3) 4. Pairs of ≅ sides (#3) 5. Pairs of ≅ angles (#4) Pairs of ≅ sides (#4) Pairs of ≅ angles (#5) Write a triangle congruence statement for each pair of triangles above 3.___________________ 4.___________________ 5.________________ Pairs of ≅ sides (#5) NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 14 M1 GEOMETRY Name:__________________________________ Period:________ Date:__________ 6. If ACB JKL, which of the following must be a correct congruence statement? A. A L C. AB JL B. B K D. BAC LKJ 7. Given that DEF JKL, mark all of the congruent corresponding parts in the diagram and then list them. D E 8. BAT J F L K COM. List each of the following. a. three pairs of congruent sides b. three pairs of congruent angles For exercises 9 – 11 list the corresponding sides and angles. Write a congruence statement. 9. Pairs of ≅ angles (#9) 10. Pairs of ≅ sides (#9) 11. Pairs of ≅ angles (#10) Pairs of ≅ sides (#10) Pairs of ≅ angles (#11) Write a triangle congruence statement for each pair of triangles above 9._________________ 10._________________ 11.___________________ Pairs of ≅ sides (#11)