GEOMETRY Chapter 4: Triangles Name: Teacher: Pd:
Table of Contents DAY 1: (Ch. 4-1 & 4-2) Pgs: 1-5 Pgs: 6-7 SWBAT: Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths. DAY 2: (Ch. 4-2) Pgs: 8-12 HW: Pgs: 13-15 SWBAT: Apply theorems about the interior and exterior angles of triangles. DAY 3: (Review) Pgs: 16-18 SWBAT: Use triangle classification to find angle measures and side lengths. Apply theorems about the interior and exterior angles of triangles. DAY 3: Take Home Quiz: Day 1 to DAY 3 DAY 4: (Ch. 4-3) Pgs: 19-24 HW: Pgs: 25-27 SWBAT: Use properties of congruent triangles. Prove triangles congruent by using the definition of congruence. DAY 5: (Ch. 4-4) Pgs: 28-33 HW: Pgs: 34-35 SWBAT: Prove triangles congruent by using SSS and SAS. DAY 6: (Ch. 4-5) Pgs: 36-40 HW: Pgs: 41-42 SWBAT: Prove triangles congruent by using ASA and AAS. DAY 7: (Ch. 4-5) Pgs: 43-46 HW: Page 47 SWBAT: Prove triangles congruent by using HL. DAY 8: (Review) Pgs: 48-50 SWBAT: Prove triangles congruent by using SSS, SAS, ASA, AAS, and HL.
Day 1: Triangle Vocabulary and Theorems Warm Up Part I: Vocabulary. Fill out the following chart below. Example 1: 1
Example 2: Example 3: Solve for x and y. Example 4: Solve for x. 2
Algebraic Problems Example 5: Example 6: Example 7: 3
Challenge Find the measure of the angle indicated. SUMMARY 4
Exit Ticket 1. 2. Sm,dndnf 5
Day 1: HW Find the missing angle 7. 8. 9. 10. 6
Find the measure of each angle of the triangle. 11. 12. 13. The angle measures of a triangle are in the ratio of 5:6:7. Find the angle measures of the triangle. 14. The angle measures of a triangle are in the ratio of 10:12:14. Find the angle measures of the triangle. 15. 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. 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 What relationship do you notice? The exterior angle of a triangle is always equal to a) 62 + 71 = m b) 23 + 27 = m c) 37 + = m (m Formula: + = 10
Part III: Practice. Apply the new theorems to solve each problem 1. Solve for x. 2. Solve for m 3. 4. Ghfhfh 11
Challenge Use the information given in the diagram to determine the m. B 4x+3 A x 2 +1 C 2x 2 +3x-2 D SUMMARY 12
Exit Ticket Day 2 HW 13
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Day 3 Review 8. 16
9. 10. 11. 12. 17
13. If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is. 14. 15. ACD is an exterior angle of ABC, m A = 3x, m ACD = 5x, and m B = 50. What is the value of x? 18
Day 4 Congruent Triangles Warm UP 1. 2. 19
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 20
Ex 2: In a congruence statement, the order of the vertices indicates the corresponding parts. Ex 3: If PQR STW, identify all pairs of corresponding congruent parts. Corresponding Sides Corresponding Angles 21
Example 4: Example 5: 22
Example 6: Example 7: ABC DEF Find the value of x Find m F. 23
Challenge SUMMARY 24
Exit Ticket Day 3 HW 25
5. 6. 7. 26
8. 9. 10. 11. 27
Warm-Up Day 4 SSS AND SAS Methods of Proving Triangles Congruent Five Ways to Prove Triangles Congruent In the previous lesson, you learned that congruent triangles have all corresponding sides and all corresponding angles congruent. Do we need to show all six parts congruent to conclude that two triangles are congruent? The answer is no. We can show triangles are congruent by showing few than all three sides and angles congruent, so long as these congruent sides and angles are in the correct order. The arrangements that prove triangles congruent are as follows: Side-Side-Side (SSS) Side-Angle-Side (SAS) Angle-Side-Angle (ASA) Angle-Angle-Side (AAS) Hypotenuse-Leg (HL) for right triangles only We will take a look at each of these in turn. Today we are going to focus on (SSS) and (SAS). 28
Mark the triangles below to prove the triangles are congruent by the SSS Theorem. Example 1: You Try! Example 2: You Try! X Y G Z 29
Example 3: You Try! a) b) 30
Mark the triangles below to prove the triangles are congruent by the SAS Theorem. Example 4: Given: Prove: ABC ZXY Example 5: Given: Prove: You Try! Given: Prove: 31
Example 6: You Example 7: 32
Challenge SUMMARY 33
Exit Ticket Day 4 HW 34
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Day 5 ASA AND AAS Methods of Proving Triangles Congruent Warm-Up For # 1-3, state if there is enough information to prove the triangles are congruent. If there is, state the theorem used and write the congruency statement. 1. 2. 3. f 36
Mark the triangles below to prove the triangles are congruent by the ASA Theorem. Example 1: Try It! Try It!: 37
fjkdfj 38
Mark the triangles below to prove the triangles are congruent by the AAS Theorem. Example 2: You Try It! You Try it! 39
SUMMARY Exit Ticket Which method proves why these two triangles are congruent? 40
Day 5 - Homework 41
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Day 6 The HL Method of Proving Triangles Congruent Warm UP 43
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what other information is needed. Examples: Practice Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what other information is needed. 44
Mark the triangles below to determine whether the HL theorem can be used to prove triangles congruent. 4. You Try! Given:,, and P Q S R 45
You Try! You Try! Given: CHALLENGE SUMMARY Exit Ticket 46
Day 6 - Homework 47
Day 7 Review of Congruent Triangles 48
DRAW A PICTURE FOR THIS SECTION! I DREW THE FIRS TWO FOR YOU. 49
Mark the triangles below to prove why the triangles are congruent by the any of the 5 Theorem. 13. 14. 15. 16. 17. 50