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Congruency of Triangles

Congruency of Triangles. 9/17/13. Warm-up 9/17/13. Tear out chapters 2, 3, and 4 and put them in your binder. Read Problem 1: Understanding Congruence p. 48. What do you think makes triangles congruent?. Congruent Line Segments.

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Congruency of Triangles

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  1. Congruency of Triangles 9/17/13

  2. Warm-up 9/17/13 • Tear out chapters 2, 3, and 4 and put them in your binder. • Read Problem 1: Understanding Congruence p. 48

  3. What do you think makes triangles congruent?

  4. Congruent Line Segments • Congruent line segments are line segments that have the same length • AB = DE

  5. Questions about Line Segments • What is the difference between the length of a line segment and a line segment? A line segment is a geometric model. The length of a line segment tells us how long the segment is numerically. • Are line segments said to be congruent or equal? Congruent • Are the lengths of line segments said to be congruent or equal? Equal

  6. Congruent Angles • Congruent angles are angles that are equal in measure.

  7. Questions about Angles • What is the difference between the measure of an angle and an angle? The measure of an angle is how big the angle is numerically. The angle is a geometric model. • Are angles said to be congruent or equal? Congruent • Are measures of angles said to be congruent or equal? Equal

  8. Congruent Triangles • Congruent triangles are triangles that are the same shape and the same size.

  9. Corresponding Sides of Congruent Triangles • Corresponding sides are sides that have the same relative positions in geometric figures. • Are corresponding sides of congruent triangles congruent? Yes! B E D A F C

  10. Corresponding Angles of Congruent Triangles • Corresponding angles are angles that have the same relative positions in geometric figures. • Are corresponding angles of congruent triangles congruent? Yes!

  11. Problem 4: Statements of Triangle Congruence p.52 Questions to think about for 1a and b: • Do you need a diagram of the triangles to determine the congruent corresponding angles? Why or why not? No, the angles are written in corresponding order. • Do you need a diagram of the triangles to determine the congruent corresponding sides? Why or why not? No, the sides are written in corresponding order.

  12. Problem 4: Statements of Triangle Congruence Questions to think about for 2 and 3: • How do you know which transformation took place? You check the corresponding angles. • Is there more than one way to write the triangle congruence statement? Explain. Yes, as long as all the sides and angles correspond, they can be written in other ways. • If the triangle congruence statement is written differently, will that change the congruent parts of the triangle? Explain. No, the triangles’ congruent parts will still correspond to each other.

  13. Closing: Talk the Talk #1 and #2 (p. 55) • Given any triangle in a coordinate plane, how can you create a different triangle that you know will be congruent to the original triangle? You can use translation, rotation, or reflection. 2. Describe the properties of congruent triangles. Congruent triangles have congruent corresponding angles and sides.

  14. Homework • Review Notes

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