Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem


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1 Name Period 10/22 11/1 Vocabulary Terms: Acute Triangle Right Triangle Obtuse Triangle Scalene Isosceles Equilateral Equiangular Interior Angle Exterior Angle 10/22 Classify and Triangle Angle Theorems 10/29 Triangle Inequalities Monday, 10/22 GEOMETRY UNIT 5 TRIANGLE PROPERTIES Auxiliary Line Vertex Side Remote Interior Angle Leg Base Base Angle Opposite 10/23 Isosceles and Equilateral 10/30 Review Vertex Angle Height Altitude Midsegment Perpendicular Bisector Angle Bisector Median Centroid 10/24 25 Special Segments 10/31 11/1 Test Incenter Orthocenter Circumcenter Inequalities Range of numbers Inscribed Circumscribed Point of Concurrency 10/26 Special Segment Proofs Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem I can classify a triangle by its sides or angles. I can solve problems involving the interior triangle sum theorem. I can solve problems involving the exterior triangle theorem ASSIGNMENT: Pg. 219 #12, 1217, 2328, & pg. 227 #2, 411, 2324, Completed: Tuesday, 10/23 Chapter 4 Section 8: Isosceles and Equilateral Triangle Properties I can solve problems using the isosceles triangle properties I can solve problems using the equilateral triangle properties. ASSIGNMENT: Pg. 276 (#17, 10, 1213, 2226, 28, 3334, 44) Completed: Wednesday or Thursday, 10/24 25 Chapter 5 Section 1 4 : All Special Segments I can solve problems using the midsegment of a triangle I can find the point(s) of concurrency of a triangle I can solve problems using the centroid, circumcenter, or incenter of a triangle. ASSIGNMENT: Special Segments in Triangles Worksheet Completed: Friday, 10/26 Chapter 5 Section 1 4 : All Special Segments I can use the coordinate plane to represent geometric figures. I can use logical reasoning to prove statements are true or find a counter example to prove them false. I can provide and recognize a valid deductive argument. ASSIGNMENT: Special Segments on a Coordinate Plane Completed:
2 Monday, 10/29 I can determine if 3 segments will make a triangle Chapter 5 Section 5 : Inequalities in 1 Triangle I can provide a range of answers given 2 sides of a triangle. I can order the sides of a triangle given the angles and order the angles given the sides. ASSIGNMENT: Pg. 336 (415, 3233, 3538, 4253, 71) Completed: Tuesday, 10/30 ASSIGNMENT: Review Worksheet Wednesday or Thursday, 10/31 11/1 Unit 5Test: Triangle Properties Review Day Test Day Completed: Grade: If you miss the review day, you are still expected to take the test on the test day. For more help BEFORE the test: 1. Use the indicated chapters in your book 2. Use the book online (it has videos and a homework help section) 3. Use Google to find more resources 4. Come to tutoring (with assignment)
3 Day 1 Classifying Triangles 1. Classify the triangles below based on their angle measures. 2. Classify the triangles below based on their side lengths. Diagram the triangles. Important Note: In an triangle, all 3 angles are. In an triangle, the are congruent.
4 Triangle Sum Theorem and Exterior Angle Theorem The sum of all angles in a triangle is. Ex: One acute angle of a right triangle measures 22.9⁰. Find the measure of the other acute angle. You Try: Find the measure of the missing angle. 37⁰ You Try: Find the measure of the missing angles. 50⁰ 47⁰ The measure of an angle of a triangle is equal to the sum of its angles. Ex: Find the measure of Ex: Find the measure of You Try: Solve for x.
5 Day 2 Objectives: Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles. Isosceles and Equilateral Triangles Vocabulary: legs of an isosceles triangle vertex angle base base angles ISOSCELES TRIANGLES Example 1: Astronomy Application The length of YX is 20 feet. Explain why the length of YZ is the same. Example 2A: Finding the Measure of an Angle Find m F. Example 2B: Finding the Measure of an Angle Find m G.
6 EQUILATERAL TRIANLGES Example 3A: Using Properties of Equilateral Triangles Find the value of x. Example 3B: Using Properties of Equilateral Triangles Find the value of y.
7 Day 3 Special Segments Practice I. Matching: Match the picture to the special segment. You will use the special segment more than once. 1) Midsegment 2) Altitude A B C D E 3) Angle Bisector 4) Perpendicular Bisector F G H I J 5) Median II. Matching: Match the point of concurrency to the special segment and to the correct fact about location. 6) Orthocenter A) Medians i) Equidistant from verticies 7) Incenter B) Altitudes ii) Equidistant from sides 8) Circumcenter C) Angle Bisectors iii) 2(small section) = (larger section) 9) Centroid D) Perpendicular Bisectors iv) No location fact III. Solve: Use the properties of special segments to solve the following problems. 10) Find WY, ZY, and XY 11) N is the circumcenter. Find QN, RN, QR ) Use the picture at the right to answer the following questions. a) A segment parallel to AC b) A segment that has half the length of AC c) A segment that has twice the length of EC 13) In the diagram of ΔABC shown below, D is the midpoint of AB, E is the midpoint of BC, and F is the midpoint of AC. If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF? A 24 B 36 C 40 D 44
8 14) G is the centroid. If CG = 20, find GE and CE? 15) In ΔABC shown below, P is the centroid and BF = 18. What is the length of BP? A 6 B 9 C 3 D 12 Use the picture to the right for 16 and ) If DF = 13, what is DE? 17) m EAD = 15 Find m<dag and m<gae 18) Find m<xrq, m<prq, and m<pqr. 19) Find n 20) Y is the circumcenter. Find YC and AB. 21) 22) The circumcenter of the triangle is equidistant from the of the triangle. 23) The incenter is important because it is from the sides of the triangle. 24) Use the picture at the right to answer the following questions. a) ST d) QR b) PU e) m<sup c) M<SUR f) m<prq
9
10 Day 4 Triangles on the Coordinate Plane Examples Ex. 1 Classify by angles and sides. Together: D(1, 0) E(3, 2) W(1, 4) You try : F(2, 1) O(1, 5) G(2, 5) Ex 2 Midsegment Together: A(3, 2) B(3, 2) C(5, 2) You try: Find the other 2 midsegments.
11 Ex. 3 Medians Together: (3, 2) (1, 6) (5, 2) You try: Find the other 2 medians. Where is the centroid? Ex 4 Altitude Together: (2, 5) (6, 5) (4,1) You try: Find the other 2 altitudes. Where is the orthocenter? Ex. 5 Perpendicular Bisectors Together: (3, 3) (3, 1) (3, 3) You try : Find the other 2 perpendicular bisectors. Where is the circumcenter?
12 Name Period Special Segments on a Coordinate Plane Classify the following triangles. Be sure to justify each classification. 1. A(1, 3) B(3, 1) C(5, 3) 2. D(2, 3) E(4, 5) F(0, 3) Using the points given, draw in each median. State the location of the centroid of each triangle. 3. G(1, 3) H(7, 1) J(3, 5) 4. K(3, 5) L(3, 1) M(5, 3) Using the points given, draw in each altitude. State the location of the orthocenter of each triangle. 5. (2, 0) (4, 0) (2, 4) 6. (3, 1) (3, 1) (1, 5)
13 Using the points given, draw in each perpendicular bisector. State the location of the circumcenter for each triangle. 7. (2, 1) (2, 3) (0, 3) 8. (3, 2) (1, 6) (5, 2) Using the points given, draw each midsegment. Then show that the midsegments are parallel and ½ the length of the sides. 9. A(1, 3) B(3, 1) C(5, 3) 10. D(2, 3) E(4, 5) F(0, 3)
14 NAME DATE PER. TRIANGLE INEQUALITY PROPERTIES NOTES Is it possible for a triangle to have sides with the following lengths? If YES, classify the triangle by its sides. 1. YES or NO Side lengths: 20, 9, 8 Classification: 2. YES or NO Side lengths: 3, 4, 5 Classification: 3. YES or NO Side lengths: 9, 12, 15 Classification: 4. YES or NO Side lengths: 6, 6, 20 Classification: Given two sides of a triangle, state the range of possible values for the third side of the triangle. 6. Side lengths: 13 and Side lengths: 6 and 21 List the segments in the following triangles shortest to longest. 8. A 70 C 65 B 10. A B C
15 11. A B C List the angles in the following triangles from largest to smallest. A C 12 B 13. Y 2 1 Z X 4
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