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Understanding Congruent Triangles and Applying SSS Congruence

This lesson introduces the concept of congruent triangles and teaches how to determine if triangles are congruent using the Side-Side-Side (SSS) congruence postulate. It also explores the properties of congruent triangles and how they can be applied in practical situations.

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Understanding Congruent Triangles and Applying SSS Congruence

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  1. Warm-Up • What does it mean for two triangles to be congruent? • If a contractor was building a house, how could she or he check to see if all of the roof trusses, which are triangles, were identical?

  2. Warm-Up • What does it mean for two triangles to be congruent? • If a contractor was building a house, how could she or he check to see if all of the roof trusses, which are triangles, were identical?

  3. 4.2 Apply Congruence and Triangles4.3 Prove Triangles Congruent by SSS Objectives: • To define congruent triangles • To write a congruent statement • To prove triangles congruent by SSS

  4. Congruent Polygons

  5. Congruent Triangles (CPCTC) Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent. • Corresponding sides are congruent • Corresponding angles are congruent

  6. Congruence Statement When naming two congruent triangles, order is very important.

  7. Example 1 Write a congruence statement for the congruent triangles below. Pay Attention to marking FAT ~ KDI

  8. Example 2 Which polygon is congruent to ABCDE? ABCDE  -?- QLMNP

  9. Example 3 Locate points I and S so that BLUE  FISH. HINT: use distance an slope to locate the new points S I

  10. Properties of Congruent Triangles

  11. Example 4 What is the relationship between <C and <F? They are corresponding and congruent

  12. Third Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

  13. Example 5 Now back to the subject of roof trusses. Would it be necessary for the manufacturer of a set of trusses to check that all the corresponding angles were congruent as well as the sides? Answer and explain in your notebook

  14. Example 5 In other words, is it sufficient that the pieces of wood (the sides of each triangle) are all the same length?

  15. Copying a Segment We’re going to try making two congruent triangles by simply copying the three sides using only a compass and a straightedge. First, let’s learn how to copy a segment.

  16. Copying a Segment • Draw segment AB.

  17. Copying a Segment • Draw a line with point A’ on one end.

  18. Copying a Segment • Put point of compass on A and the pencil on B. Make a small arc.

  19. Copying a Segment • Put point of compass on A’ and use the compass setting from Step 3 to make an arc that intersects the line. This is B’.

  20. Copying a Segment Click on the button to watch a video of the construction.

  21. Investigation 1 Now apply the construction for copying a segment to copy the three sides of a triangle.

  22. Investigation 1 • Use your straight edge to construct a triangle. • Now draw a line with A’ on one end.

  23. Investigation 1 • Copy segment AB onto your line to make A’B’.

  24. Investigation 1 • Put point of compass on A and pencil on C. Copy this distance from A’.

  25. Investigation 1 • Put point of compass on B and pencil on C. Copy this distance from B’. This is C’

  26. Investigation 1 • Finish your new triangle by drawing segments A’C’ and B’C’.

  27. Side-Side-Side Congruence Postulate SSS Congruence Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

  28. SSS Congruence Postulate

  29. Example 6 Decide whether the triangles are congruent. Explain your reasoning. Answer in your notebook

  30. Example 7 ~ • AC = AD Given • BC = BD • 2. AB = AB Transitive Prop. • 3.. ABC = ABD SSS ~ ~ ~

  31. Example 8 Explain why the bench with the diagonal support is stable, while the one without the support can collapse.

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