1 / 48

Chapter 5 Applying Congruent Triangles

Chapter 5 Applying Congruent Triangles. Warm Up For Chapter 5. 5.1 Special Segments in Triangles. 5.1 Day 2 Proofs. 5.2 Right Triangles Internet Activity. 5.1 Special Segments in Triangles.

trixie
Download Presentation

Chapter 5 Applying Congruent Triangles

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. Chapter 5Applying Congruent Triangles Warm Up For Chapter 5 5.1 Special Segments in Triangles 5.1 Day 2 Proofs 5.2 Right Triangles Internet Activity

  2. 5.1 Special Segments in Triangles Objective: Identify and use medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle Click Me!! How will I use this? Special segments are used in triangles to solve problems involving engineering, sports and physics. Angle Bisector Median Perpendicular Bisector Altitude Chapter 5 An example to tie it all together

  3. Definitions Median A segment that connects a vertex of a triangle to themidpoint of the side opposite the vertex.

  4. Definitions Altitude A line segment with 1 endpoint at a vertex of a triangle and the other on the line opposite that vertex so that the line segment is perpendicular to the side of the triangle.

  5. Definitions Perpendicular Bisector: A line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side. Perpendicular Bisector Theorems!

  6. Theorems Theorem 5.1: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Theorem 5.2: Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment. Angle Bisector Chapter 5 Median Perpendicular Bisector Altitude

  7. Theorems Theorem 5.3: Any point on the bisector of an angle is equidistant from the sides of the angle. Theorem 5.4: Any point on or in the interior of an angle and equidistant from the sides of an angle lies on the bisector of the angle. Angle Bisector Chapter 5 Median Perpendicular Bisector Altitude

  8. Warm UP In Find the value of x and the measure of each angle. Answer

  9. Warm Up Answers How did I get that? Click the answer to see! BONUS!!! What type of triangle is ABC? Click me to find the Answer!! Section 5.1

  10. BONUS!!! What type of triangle is ABC? Click me to find the Answer!!

  11. Because the question give you angle measures, we take the sum of the angles and set them equal to 180. } } } BONUS!! Click Me!! Combine like terms! Add 20 to both sides! Divide by 10 on both sides! Section 5.1 Chapter 5

  12. Use substitution for the answer you found for x and plug it into the equation for angle A. BONUS!! Click Me!! Section 5.1 Chapter 5

  13. Use substitution for the answer you found for x and plug it into the equation for angle B. BONUS!! Click Me!! Section 5.1 Chapter 5

  14. Use substitution for the answer you found for x and plug it into the equation for angle C. BONUS!! Click Me!! Section 5.1 Chapter 5

  15. Triangle ABC is a right isosceles triangle Why is that?? Section 5.1 Chapter 5

  16. Angle Bisector What is an Angle Bisector? Click me to find out! Move my vertices around and see what happens!! Angle Bisector Theorems Example Section 5.1

  17. Median Example Draw the three medians of triangle ABC. Name each of them. B Answer C A

  18. Median Example Draw the three medians of triangle ABC. Name each of them. B F D C A E Back to Section 5.1

  19. Altitude Example Draw the three altitudes, QU, SV, and RT. R Answer S Q

  20. Altitude Example Draw the three altitudes, QU, SV, and RT. V U R T S Q Back to Section 5.1

  21. Perpendicular Bisector Example Draw the three lines that are perpendicular bisectors of XYZ. Y Answer X Z Label the lines l,m, and n.

  22. Perpendicular Bisector Example Draw the three lines that are perpendicular bisectors of XYZ. Y m l X n Z Back to Section 5.1

  23. Angle Bisector Example If BD bisects ABC, find the value of x and the measure of AC. B C A D Answer

  24. Angle Bisector Example If BD bisects ABC, find the value of x and the measure of AC. B Show me how you got those answers! C A D Back to Section 5.1

  25. Angle Bisector Example If BD bisects ABC, find the value of x and the measure of AC. Means that the angle is split into 2 congruent parts. Set the two angles equal to each other and solve. Once you find x, plug it into AD and DC. Since you are looking for the total length, AC, use segment addition to find the total length. B C A D Back to Section 5.1

  26. 5.1 Proofs Together YOU TRY!!!

  27. Given: Just keep clicking! Prove: 5. SAS 1. Given 7 4 1 2 1 5 6 3 2. Def of Isos Triangle 6. CPCTC 7. Def of Median 3. Def of Angle Bisector 5.1 Proofs 4. Reflexive

  28. Given: Just keep clicking! Prove: 5. SAS 1. Given 4 1 1 2 7 5 6 3 2. Def of Equilateral Triangle 6. CPCTC We’re done, take me back to the beginning! 7. Def of Median 3. Def of Angle Bisector 4. Reflexive

  29. Example Keep clicking to see graph! S G B median Midpoint See the Work!!

  30. What is the Midpoint Formula? Midpoint of GB Just keep clicking! Next Question

  31. Just keep clicking! What can we conclude? We’re done, take me back to the beginning!

  32. 5.2 Right Triangles An Internet Activity CLICK TO BEGIN

  33. Click on the triangle and learn about the Theorems or Postulates. Take notes as you read along with each Theorem or Postulate!! Click me when done

  34. Examples I finished! Click me!!

  35. Solve for… Example 1 Example 2 Example 3

  36. State the additional information.

  37. P D F E Q R Answer

  38. Next Example

  39. E F D Q R P Answer

  40. Next Example

  41. F E P D Q R Answer

  42. Back to Beginning

  43. State the additional information needed to prove the pair of triangles congruent by LA. J M K L Answer

  44. Proving triangles congruent by LA means a leg and an angle of the right triangle must be congruent. J K M OR L Next Example

  45. State the additional information needed to prove the pair of triangles congruent by HA. S Z T X Y V Answer

  46. State the additional information needed to prove the pair of triangles congruent by HA. S The keyword was additional. When proving triangles congruent by HA, all that is needed is to show that the hypotenuse is congruent on each triangle as well as an acute angle. In these triangles both are already shown so there is no ADDITIONAL information needed. Z T X Y V Next Example

  47. State the additional information needed to prove the pair of triangles congruent by LA. B C D A Answer F

  48. State the additional information needed to prove the pair of triangles congruent by LA. B C D OR A F Back to Beginning

More Related