Geometry Regents: Unit 5 Triangles Name:_____________________________ Teacher:____________________________ Pd: _______ Table of Contents DAY 1: (Ch. 4-1 & 4-2) SWBAT: Classify triangles by their angle measures and side lengths. Pgs: 1-5 Use triangle classification to find angle measures and side lengths. Pgs: 6-7 DAY 2: (Ch. 4-2) SWBAT: Apply theorems about the interior and exterior angles of triangles. Pgs: 8-12 HW: Pgs: 13-15 DAY 3: (Ch. 4-8) SWBAT: Apply Properties of Equilateral and Isosceles Triangles. Pgs: 16-21 HW: Pgs: 22-23 DAY 4: SWBAT: Construct isosceles and equilateral triangles using a compass and a straight edge Pgs: 24-27 HW: Pgs: 28-30 DAY 5: (Ch. 4-3) SWBAT: Use properties of congruent triangles to solve for missing sides and/or angles Pgs: 31-36 Prove triangles congruent by using the definition of congruence. HW: Pgs: 37-39 DAY 6: (Ch. 4-4 to 4-5) SWBAT: Prove triangles congruent by using SSS, SAS, ASA, AAS, and HL. Pgs: 40-42 HW: Pgs: 43-44 REVIEW Pgs: 45-56 Day 1: Sum of Interior Angles of Triangles Warm – Up Classifying Triangles by their Sides 1 m 1 = _____ m 2 = _____ m 3 = _____ Practice – Find the missing angle 1) 2) 3) Algebraic Problems Practice: Practice: 2 Example 3: Example 4: The ratio of the measures of the angles of a triangle is 4:5:6. Find the measure of the angles and classify the triangle as acute, right, or obtuse. Practice: Practice Practice 3 Challenge Find the measure of the angle indicated. SUMMARY 4 Exit Ticket 1. 2. 5 Day 1: HW 6 13. The angle measures of a triangle are in the ratio of 5:6:7. Find the angle measures of the triangle. 14. 15. 16. If the measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x − 6, the triangle must be: 1) Isosceles 2) Equilateral 3) Right 4) Scalene 7 Day 2: Exterior Angles of Triangles Warm - UP 1. Find the measure of the missing angles. 2. 8 Part I: Angle relationships in triangles. Find the measure of all angles in the triangles below. Then answer the following questions and try to develop the theorems that represent these relationships. After checking the theorems with your teacher, then complete the remaining examples. a) b) c) 9 Part II: Conclusions 1. Investigate the Triangle Sum Theorem and its corollaries a) 62 + 71 + _____ = _____ (m b) 23 + 27 + _____ = _____ (m c) 90 + 37 + _____ = _____ (m In any triangle, the sum of the interior angles is equal to ___________ In a right triangle, the two acute angles are _________________. In an equiangular triangle, all angles measure ___________ 2. Investigate the Exterior Angles Theorem a) 62 + 71 = _____ m b) 23 + 27 = _____ m c) 37 + ______ = _____ m (m What relationship do you notice? The exterior angle of a triangle is always equal to Formula: ____ + _____ = ______ 10 Part III: Practice. Apply the new theorems to solve each problem 1. Solve for x. 2. 3. 4. Solve for m 11 B Challenge 4x+3 Use the information given in the diagram to determine the m . x2+1 2x2+3x-2 A C D SUMMARY Exit Ticket 12 Day 2 – HW 13 14 15 Day 3 – The Isosceles and Equilateral Triangle Warm – Up Find the measure of the missing angles 16 If all the angles are congruent in a triangle, then the measure of each angle is ___________. Example 1 – Find the value of x Practice: 2. Find the value of OP. 17 Example 1: Example 2: Finding the Measure of an Angle a. a. 80 b. 55 18 Example 3: a. 40 b. 150 Example 4: Finding the Measure of an Angle Find mG. Practice: Finding the Measure of an Angle Find mN. 19 Example 5: Finding the Measure of an Angle Practice Word Problem: Finding the Measure of an Angle 20 Challenge Find the value of x. Exit Ticket 1. 2. 21 Day – 3 - Homework 1. 2. 3. 4. 5. 6. 22 11. 12. 13. 23 Day 4 – Constructions SWBAT: Construct isosceles and equilateral triangles using a compass and a straight edge Warm – Up 24 Student Practice 25 A) B) 26 Challenge Problem Exit Ticket 27 Homework – Day 4 Construct an isosceles triangle given the length of the base and the length of the sides. 1) 2) 28 3) 4) 29 5) 30 Day 5 – Congruent Triangles Warm – UP 1. 2. 31 Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same _______________ in polygons with an equal number of _______. Two polygons are _________ polygons if and only if their _________________ sides are _____________. Thus triangles that are the same size and shape are congruent. Ex 1: Name all the corresponding sides and angles below if Corresponding Sides Corresponding Angles 32 Ex 2: Ex 3: 33 Example 4: Example 5: 34 Example 6: Example 7: ∆ABC ∆DEF Find the value of x Find mF. 35 Challenge SUMMARY \\ Exit Ticket 36 Day 5 – HW 37 5. 6. 7. 38 8. 9. 10. 11. 39 Day 6 – Proving Triangles Congruent DO NOW Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be used to prove the triangles congruent. Example 1: _____________________ _____________________ 40 Practice Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be used to prove the triangles congruent. a) b) c) d) e) f) _________ ___________ ___________ ___________ __________ _________ 41 Challenge Problem Exit Ticket 42 HOMEWORK Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be used to prove the triangles congruent. 1)________________________ 2)____________________ 3)_____________________ 4)________________________ 5)______________________ 6)_____________________ 7)________________________ 8)______________________ 9)_____________________ 10)________________________ 11)____________________ 12)____________________ 43 13)________________________ 14)____________________ 15)_____________________ 16)________________________ 17)____________________ 18)_____________________ 19)________________________ 20)____________________ 21)_____________________ 22)________________________ 23)____________________ 24)_____________________ 44 Day 7 – Review for Test a. b. c. d. 45 e. f. g. 46 h. I. J. In ABC, is extended to D, m B = 2y, m BCA = 6y, and m ACD = 3y. What is m A? 47 K. L. M-N. 48 O. Given: ̅̅̅ ̅ ̅ ̅̅̅ ̅ ̅̅̅ ̅ ̅̅̅ ̅ P. 49 Q. Given: ∆JKM ∆ _______ because of ______. R. ∆XWZ ∆ _______ because of ______. S. 50 Determine if you can use SSS, SAS, ASA, and AAS to prove triangles congruent. If not, say no. Identifying Additional Congruent Parts A. AN OM B. DA MO C. ND TO D. DA TO a. A O b. N M c. DA TO d. A M 51 a. O N b. c. d. NA MO a. EL KA b. C J c. E K d. L A A O A M 52 3. 4. 53 7. In the accompanying diagram of BCD, ABC is an equilateral triangle and AD = AB. What is the value of x, in degrees? 54 Word Problems 1. 2. 3. F 4. 55 CONSTRUCTIONS Construct an isosceles triangle given the length of the base and the length of the sides. 56 57 .