1 / 37

Triangle Theorems & Proportional Segments Lesson Menu

Explore Triangle Proportionality, Midsegment Theorem, and Parallel Lines. Verify triangle similarities, solve real-world problems, and prove relationships. Dive into geometric figures with examples and exercises.

trinkle
Download Presentation

Triangle Theorems & Proportional Segments Lesson Menu

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Splash Screen

  2. Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Theorem 7.5: Triangle Proportionality Theorem Example 1: Find the Length of a Side Theorem 7.6: Converse of Triangle Proportionality Theorem Example 2: Determine if Lines are Parallel Theorem 7.7: Triangle Midsegment Theorem Example 3: Use the Triangle Midsegment Theorem Corollary 7.1: Proportional Parts of Parallel Lines Example 4: Real-World Example: Use Proportional Segments of Transversals Corollary 7.2: Congruent Parts of Parallel Lines Example 5: Real-World Example: Use Congruent Segments of Transversals Lesson Menu

  3. Determine whether the triangles are similar. Justify your answer. A. yes, SSS Similarity B. yes, ASA Similarity C. yes, AA Similarity D. No, sides are not proportional. 5-Minute Check 1

  4. Determine whether the triangles are similar. Justify your answer. A. yes, AA Similarity B. yes, SSS Similarity C. yes, SAS Similarity D. No, sides are not proportional. 5-Minute Check 2

  5. Determine whether the triangles are similar. Justify your answer. A. yes, AA Similarity B. yes, SSS Similarity C. yes, SAS Similarity D. No, angles are not equal. 5-Minute Check 3

  6. Find the width of the river in the diagram. A. 30 m B. 28 m C. 24 m D. 22.4 m 5-Minute Check 4

  7. Content Standards G.SRT.4 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS

  8. You used proportions to solve problems between similar triangles. • Use proportional parts within triangles. • Use proportional parts with parallel lines. Then/Now

  9. midsegment of a triangle Vocabulary

  10. Concept

  11. Find the Length of a Side Example 1

  12. Find the Length of a Side Substitute the known measures. Cross Products Property Multiply. Divide each side by 8. Simplify. Example 1

  13. A. 2.29 B. 4.125 C. 12 D. 15.75 Example 1

  14. Concept

  15. In order to show that we must show that Determine if Lines are Parallel Example 2

  16. Since the sides are proportional. Answer: Since the segments have proportional lengths, GH || FE. Determine if Lines are Parallel Example 2

  17. A. yes B. no C. cannot be determined Example 2

  18. Concept

  19. A. In the figure, DE and EF are midsegments of ΔABC. Find AB. Use the Triangle Midsegment Theorem Example 3

  20. ED = AB Triangle Midsegment Theorem 5 = AB Substitution 1 1 __ __ 2 2 Use the Triangle Midsegment Theorem 10 = AB Multiply each side by 2. Answer:AB = 10 Example 3

  21. B. In the figure, DE and EF are midsegments of ΔABC. Find FE. Use the Triangle Midsegment Theorem Example 3

  22. FE = BC Triangle Midsegment Theorem FE = (18) Substitution 1 1 __ __ 2 2 Use the Triangle Midsegment Theorem FE = 9 Simplify. Answer:FE = 9 Example 3

  23. C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE. Use the Triangle Midsegment Theorem Example 3

  24. By the Triangle Midsegment Theorem, AB || ED. Use the Triangle Midsegment Theorem AFEFED Alternate Interior Angles Theorem mAFE = mFED Definition of congruence mAFE = 87 Substitution Answer:mAFE= 87 Example 3

  25. A. In the figure, DE and DF are midsegments of ΔABC. Find BC. A. 8 B. 15 C. 16 D. 30 Example 3

  26. B. In the figure, DE and DF are midsegments of ΔABC. Find DE. A. 7.5 B. 8 C. 15 D. 16 Example 3

  27. C. In the figure, DE and DF are midsegments of ΔABC. Find mAFD. A. 48 B. 58 C. 110 D. 122 Example 3

  28. Concept

  29. Use Proportional Segments of Transversals MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x. Example 4

  30. Use Proportional Segments of Transversals Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Triangle Proportionality Theorem Cross Products Property Multiply. Divide each side by 13. Answer:x = 32 Example 4

  31. In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x. A. 4 B. 5 C. 6 D. 7 Example 4

  32. Concept

  33. Use Congruent Segments of Transversals ALGEBRA Find x and y. To find x: 3x – 7 = x + 5 Given 2x – 7 = 5 Subtract x from each side. 2x = 12 Add 7 to each side. x = 6 Divide each side by 2. Example 5

  34. Use Congruent Segments of Transversals To find y: The segments with lengths 9y – 2 and 6y + 4 are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal. Example 5

  35. Use Congruent Segments of Transversals 9y – 2 = 6y + 4 Definition of congruence 3y – 2 = 4 Subtract 6y from each side. 3y = 6 Add 2 to each side. y = 2 Divide each side by 3. Answer:x = 6; y = 2 Example 5

  36. A. ; B.1; 2 C.11; D.7; 3 2 3 __ __ 3 2 Find a and b. Example 5

  37. End of the Lesson

More Related