1 / 40

Splash Screen

Splash Screen. Classify the triangle. A. scalene B. isosceles C. equilateral. 5-Minute Check 1. Find x if m A = 10 x + 15 , m  B = 8 x – 18 , and mC = 12 x + 3. A. 3.75 B. 6 C. 12 D. 16.5. 5-Minute Check 2.

weirl
Download Presentation

Splash Screen

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. Classify the triangle. A. scalene B. isosceles C. equilateral 5-Minute Check 1

  3. Find x if mA = 10x + 15, mB = 8x – 18, andmC = 12x + 3. A. 3.75 B. 6 C. 12 D. 16.5 5-Minute Check 2

  4. Name the corresponding congruent angles if ΔRST ΔUVW. A. R  V,S  W,T  U B. R  W,S  U,T  V C. R  U,S  V,T  W D. R  U,S  W,T  V 5-Minute Check 3

  5. A. B. C. D. , Name the corresponding congruent sides if ΔLMN ΔOPQ. 5-Minute Check 4

  6. Find y if ΔDEF is an equilateral triangle and mF = 8y + 4. A. 22 B. 10.75 C. 7 D. 4.5 5-Minute Check 5

  7. ΔABC has vertices A(–5, 3) and B(4, 6). What are the coordinates for point C if ΔABC is an isosceles triangle with vertex angle A? A. (–3, –6) B. (4, 0) C. (–2, 11) D. (4, –3) 5-Minute Check 6

  8. Content Standards G.CO.10 Prove theorems about triangles. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS

  9. You used segment and angle bisectors. • Identify and use perpendicular bisectors in triangles. • Identify and use angle bisectors in triangles. Then/Now

  10. perpendicular bisector - in a triangle, a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side. • concurrent lines - three or more lines that intersect at a common point. • point of concurrency - the point of intersection of concurrent lines. Vocabulary

  11. Circumcenter - the point of concurrency of the perpendicular bisectors of a triangle. • Incenter - the point of concurrency of the angle bisectors of a triangle.

  12. Concept

  13. Use the Perpendicular Bisector Theorems A. Find BC. BC = AC Perpendicular Bisector Theorem BC = 8.5 Substitution Answer: 8.5 Example 1

  14. Use the Perpendicular Bisector Theorems B. Find XY. Answer: 6 Example 1

  15. Use the Perpendicular Bisector Theorems C. Find PQ. PQ = RQ Perpendicular Bisector Theorem 3x + 1 = 5x – 3 Substitution 1 = 2x – 3 Subtract 3x from each side. 4 = 2x Add 3 to each side. 2 = x Divide each side by 2. So, PQ = 3(2) + 1 = 7. Answer: 7 Example 1

  16. A. Find NO. A. 4.6 B. 9.2 C. 18.4 D. 36.8 Example 1

  17. B. Find TU. A. 2 B. 4 C. 8 D. 16 Example 1

  18. C. Find EH. A. 8 B. 12 C. 16 D. 20 Example 1

  19. Concept

  20. Use the Circumcenter Theorem GARDEN A triangular-shaped garden is shown. Can a fountain be placed at the circumcenter and still be inside the garden? By the Circumcenter Theorem, a point equidistant from three points is found by using the perpendicular bisectors of the triangle formed by those points. Example 2

  21. Use the Circumcenter Theorem Copy ΔXYZ, and use a ruler and protractor to draw the perpendicular bisectors. The location for the fountain is C, the circumcenter of ΔXYZ, which lies in the exterior of the triangle. C Answer: Example 2

  22. Use the Circumcenter Theorem Copy ΔXYZ, and use a ruler and protractor to draw the perpendicular bisectors. The location for the fountain is C, the circumcenter of ΔXYZ, which lies in the exterior of the triangle. C Answer: No, the circumcenter of an obtuse triangle is in the exterior of the triangle. Example 2

  23. BILLIARDSA triangle used to rack pool balls is shown. Would the circumcenter be found inside the triangle? A. No, the circumcenter of an acute triangle is found in the exterior of the triangle. B. Yes, circumcenter of an acute triangle is found in the interior of the triangle. Example 2

  24. BILLIARDSA triangle used to rack pool balls is shown. Would the circumcenter be found inside the triangle? A. No, the circumcenter of an acute triangle is found in the exterior of the triangle. B. Yes, circumcenter of an acute triangle is found in the interior of the triangle. Example 2

  25. Concept

  26. Use the Angle Bisector Theorems A. Find DB. DB = DC Angle Bisector Theorem DB = 5 Substitution Answer:DB = 5 Example 3

  27. Use the Angle Bisector Theorems B. Find mWYZ. Example 3

  28. Use the Angle Bisector Theorems WYZ  XYW Definition of angle bisector mWYZ = mXYW Definition of congruent angles mWYZ = 28 Substitution Answer:mWYZ = 28 Example 3

  29. Use the Angle Bisector Theorems C. Find QS. QS = SR Angle Bisector Theorem 4x – 1 = 3x + 2 Substitution x – 1 = 2 Subtract 3x from each side. x = 3 Add 1 to each side. Answer: So, QS = 4(3) – 1 or 11. Example 3

  30. A. Find the measure of SR. A. 22 B. 5.5 C. 11 D. 2.25 Example 3

  31. B. Find the measure of HFI. A. 28 B. 30 C. 15 D. 30 Example 3

  32. C. Find the measure of UV. A. 7 B. 14 C. 19 D. 25 Example 3

  33. Concept

  34. Use the Incenter Theorem A. Find ST if S is the incenter of ΔMNP. By the Incenter Theorem, since S is equidistant from the sides of ΔMNP,ST = SU. Find ST by using the Pythagorean Theorem. a2 + b2 = c2 Pythagorean Theorem 82 + SU2 = 102 Substitution 64 + SU2 = 100 82 = 64, 102 = 100 Example 4

  35. Use the Incenter Theorem SU2 = 36 Subtract 64 from each side. SU = ±6 Take the square root of each side. Since length cannot be negative, use only the positive square root, 6. Since ST = SU, ST = 6. Answer:ST = 6 Example 4

  36. Since MS bisects RMT, mRMT = 2mRMS. So mRMT = 2(31) or 62. Likewise, mTNU = 2mSNU, so mTNU = 2(28) or 56. Use the Incenter Theorem B. Find mSPU if S is the incenter of ΔMNP. Example 4

  37. Since PS bisects UPR, 2mSPU = mUPR. This means that mSPU = mUPR. 1 1 __ __ 2 2 Answer:mSPU = (62) or 31 Use the Incenter Theorem mUPR + mRMT + mTNU = 180 Triangle Angle Sum Theorem mUPR + 62 + 56 = 180 Substitution mUPR + 118 = 180 Simplify. mUPR = 62 Subtract 118 from each side. Example 4

  38. A. Find the measure of GF if D is the incenter of ΔACF. A. 12 B. 144 C. 8 D. 65 Example 4

  39. B. Find the measure of BCD if D is the incenter of ΔACF. A. 58° B. 116° C. 52° D. 26° Example 4

  40. End of the Lesson

More Related