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Lesson 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ M2 Period: ________ Date: __________ Lesson 2: Triangle Side- Splitter Learning Target: I can use the side splitter theorem, which states that a segment splits two sides of a triangle proportionally if and only if it is parallel to the third side to find the missing sides. Previously we learned β¦. There are two properties of scale drawing/dilations of a figure: 1. Corresponding angles are ________________ in measurement 2. Corresponding lengths and sides are _____________________ in measurement. Opening Exercise Using the ratio method to dilate triangle ABC by the rule π«π¨,π . Using a box as 1 unit find each of the following measurements AC = ______ AB = ______ BC= ________ ACβ = ______ ABβ= ______ BβCβ= _______ Fill in the following proportional statement π΄πΆβ² = π΄π΅β² = π΅πΆ = Consider the following measurements find the measures of the other two angles πβ π΅ = 60 πβ π΅β² = ______ πβ πΆ = 30 πβ πΆβ² = ______ If ______________________________ angles are congruent then segment BC ____ BβCβ. What can we say about the following ratios? π΄πΆ = __________ πΆπΆβ² π΄π΅ π΅π΅β² = _______ Conclusion: When a segment is created in a triangle such that the segment is parallel to the third side, then it divides the other sides proportionally. This segment is called side splitter. Lesson 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ M2 Period: ________ Date: __________ Triangle side splitter theorem: A line segment splits two sides of a triangle proportionally if and only if it is parallel to the third side. Restatement of the triangle side splitter theorem: In βOAβ²Bβ², Μ Μ Μ Μ splits the sides proportionally AB = or = if and only if ___________|| ___________ Use the side-splitter theorem to solve for x in the triangles below. 1. Show your work 2. Try on your own ( 4 mins) 3. Given the diagram, π΄πΆ = 12, π΄π΅ = 6, π΅πΈ = 4, πβ π΄πΆπ΅ = 28°, and πβ π· = 28° What is the relationship between segment CB and DE? Explain why? What can you say about the following ratios? Explain your reasoning π΄πΆ π΄π· π΄π΅ π΄πΈ πΆπ΅ π·πΈ Find the length of AD ___________ Find the length of CD ___________ Lesson 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ M2 Period: ________ Date: __________ Lesson 2: Triangle Side- Splitter Problem Set Μ Μ Μ Μ Μ a side-splitter? Justify your answer with algebraic work and a written 1. Is line segment ππ explanation. Μ Μ Μ Μ . Use the diagram to answer the following Problems 2 & 3: Μ Μ Μ Μ β₯ π΄πΆ In the diagram at right, ππ 2. If π΅π = 4, π΅π΄ = 5, and π΅π = 6, what is π΅πΆ? 3. If π΅π = 9, π΅π΄ = 15, and π΅π = 15, what is ππΆ? Not drawn to scale Use the side-splitter theorem to solve for x in each of the diagrams below. 4. 5. NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ Lesson 2 M2 Period: ________ Date: __________ Μ Μ Μ Μ , π΄π· = 3, π·π΅ = 2, πππ π·πΈ = 6 . Find the length of 6. In the diagram of βπ΄π΅πΆ below, Μ Μ Μ Μ π·πΈ β₯ π΅πΆ Μ Μ Μ Μ π΅πΆ . Μ Μ Μ Μ β₯ Μ Μ Μ Μ 7. In the diagram below of βπ΄π·πΈ, B is a point on Μ Μ Μ Μ π΄πΈ and C is a point on Μ Μ Μ Μ π΄π· such that π΅πΆ πΈπ· , Μ Μ Μ Μ . π΄πΆ = π₯ β 3, π΅πΈ = 20, π΄π΅ = 16, and π΄π· = 2π₯ + 2 . Find the length of π΄πΆ 8. In βπ΄π΅πΆ , Μ Μ Μ Μ π·πΈ is drawn parallel to Μ Μ Μ Μ π΄πΆ . Using the a ruler, determine the lengths AD, DB, CE, EB, DE, and AC in millimeters. Use these lengths to form ratios and to determine if there is a relationship between any of the ratios. What can you say about segment Μ Μ Μ Μ π·πΈ ? Lesson 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ M2 Period: ________ Date: __________ Lesson 2: Triangle Side- Splitter Homework Use the side-splitter theorem to solve for x in each of the diagrams below. 1. 2. 3. 4. 5. 6. NYS COMMON CORE MATHEMATICS CURRICULUM Name:__________________________________ Lesson 2 M2 Period: ________ Date: __________