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Warm Up

This lesson focuses on identifying congruent figures and triangles and using congruence to solve problems. Students will participate in warm-up activities, complete textbook examples, and work on class and group assignments. The lesson concludes with a math journal reflection and a lesson quiz.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Math Journal (5 Min) • “What Do I Know About” – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they know about the lesson before they have been taught the lesson, and at the end of class, write about what they now know about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they now know that pertained to the lesson.

  3. Homework Review (5 Min)

  4. Warm Up Find the measure of the third angle in the triangle, given two angle measures. 1. 58°, 104° 2. 32°, 63° 3. 90°, 38° 4. 42°, 88° 18° 85° 52° 50°

  5. Problem of the Day Draw triangles ABC and DEF so that a.AB = DE and BC = EF b. angle A is congruent to angle D. c. the triangles are not congruent.

  6. Textbook Examples (I Do) (5 Min)

  7. Learn to identify congruent figures and to use congruence to solve problems.

  8. Vocabulary Side-Side-Side Rule

  9. Which center circle do you think is bigger? In spite of appearances, the two center circles are congruent. Their apparent differences are optical illusions. One way to determine whether figures are congruent is to see if one figure will fit exactly over the other one. Look at the two patterns.

  10. Additional Example 1A: Identifying Congruent Figures in the Real World Identify any congruent figures. The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure.

  11. Additional Example 1B: Identifying Congruent Figures in the Real World Identify any congruent figures. The sectors in the figure are congruent.

  12. Check It Out: Example 1A Identify any congruent figures. The sides of the figures are are not congruent.

  13. Check It Out: Example 1B Identify any congruent figures. The figures are not congruent. The figure on the outside is larger than the one on the inside.

  14. If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles, if the corresponding sides are congruent, then the corresponding angles will always be congruent. This is called the Side-Side-Side Rule. Because of this rule, when determining whether triangles are congruent, you only need to determine whether the sides are congruent.

  15. Additional Example 2: Identifying Congruent Triangles Determine whether the triangles are congruent. Q C 4 cm 4 cm AB = 4 cm BC = 4 cm AC = 6 cm PQ = 4 cm PR = 4 cm RQ = 5 cm B P 5 cm 6 cm 4 cm 4 cm R A The triangles are not congruent. Although two sides in one triangle are congruent to two sides in the other, the third sides are not congruent.

  16. By the Side-Side-Side Rule, ABC is congruent to DEF, or ABCDEF. If you flip one triangle, it will fit exactly over the other. Reading Math The notation ABC is read “triangle ABC.” Check It Out: Example 2 Determine whether the triangles are congruent. AC = 8 m AB = 6 m BC = 10 m DF = 8 m DE = 6 m EF = 10 m B E 10 m 10 m 6 m 6 m A C D F 8 m 8 m

  17. For polygons with more than three sides, it is not enough to compare the measures of their sides. For example, the corresponding sides of the figures below are congruent, but the figures are not congruent. If you know that two figures are congruent, you can find the missing measures in the figures.

  18. Additional Example 3: Using Congruence to Find Unknown Measures Determine the unknown measure in the set of congruent polygons. The corresponding parts of congruent polygons are congruent. The unknown angle measure is 110°. The unknown side length is 28 mm.

  19. Check It Out: Example 3A Determine the unknown measure in the set of congruent polygons. ? The corresponding sides are congruent. 135° 5 ft 120° 6 ft 45° 60° The unknown side length is 4 ft. 8 ft 8 ft 60° 45° 6 ft 135° 5 ft 120° 4 ft

  20. Check It Out: Example 3B Determine the unknown measure in the set of congruent polygons. 6 ft 5 ft The corresponding angles are congruent. 130° 110° 8 ft 120° 80° 4 ft 100° 10 ft The unknown angle measure is 130°. 10 ft 100° 4 ft 80° 120° 8 ft 110° ? 5 ft 6 ft

  21. Class work Problems (We Do) (10 Min) • Pg. 338-339 (1-7)

  22. Small Group CW(Yall Do) (10 Min) • Pg. 338-339 (8-22 EOE)

  23. Homework (You Do) (10 Min) • Pg. 338-339 (9, 11, 13, 15, 19 odd)

  24. Math Journal (5 Min) • “What Do I Know About” – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they know about the lesson before they have been taught the lesson, and at the end of class, write about what they now know about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they now know that pertained to the lesson.

  25. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  26. Lesson Quiz 1. Identify any congruent figures. none 2. Determine the unknown measures in the set of congruent polygons. a = 11, b = 6, c = 110°

  27. Lesson Quiz for Student Response Systems • 1. Identify the congruent triangles. • A. B.

  28. Lesson Quiz for Student Response Systems • 2. Identify the missing measures in the set of congruent polygons. • A. a = 6, b = 9, c = 40° • B.a = 9, b = 6, c = 40° • C.a = 9, b = 6, c = 60° • D.a = 6, b = 9, c = 60°

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