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Lesson Menu Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Theorem 7.5: Triangle Proportionality Theorem Example 1: Find the Length of a Side Theorem 7.6: Converse of Triangle Proportionality Theorem Example 2: Determine if Lines are Parallel Theorem 7.7: Triangle Midsegment Theorem Example 3: Use the Triangle Midsegment Theorem Corollary 7.1: Proportional Parts of Parallel Lines Example 4: Real-World Example: Use Proportional Segments of Transversals Corollary 7.2: Congruent Parts of Parallel Lines Example 5: Real-World Example: Use Congruent Segments of Transversals
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Over Lesson 7–3 5-Minute Check 1 A.yes, SSS Similarity B.yes, ASA Similarity C.yes, AA Similarity D.No, sides are not proportional. Determine whether the triangles are similar. Justify your answer.
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Over Lesson 7–3 5-Minute Check 2 A.yes, AA Similarity B.yes, SSS Similarity C.yes, SAS Similarity D.No, sides are not proportional. Determine whether the triangles are similar. Justify your answer.
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Over Lesson 7–3 5-Minute Check 3 A.yes, AA Similarity B.yes, SSS Similarity C.yes, SAS Similarity D.No, angles are not equal. Determine whether the triangles are similar. Justify your answer.
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Over Lesson 7–3 5-Minute Check 4 A.30 m B.28 m C.24 m D.22.4 m Find the width of the river in the diagram.
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CCSS Content Standards G.SRT.4 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.
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Then/Now You used proportions to solve problems between similar triangles. Use proportional parts within triangles. Use proportional parts with parallel lines.
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Vocabulary midsegment of a triangle
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Concept
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Example 1 Find the Length of a Side
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Example 1 Find the Length of a Side Substitute the known measures. Cross Products Property Multiply. Divide each side by 8. Simplify.
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Example 1 A.2.29 B.4.125 C.12 D.15.75
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Concept
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Example 2 Determine if Lines are Parallel In order to show that we must show that
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Example 2 Determine if Lines are Parallel Since the sides are proportional. Answer: Since the segments have proportional lengths, GH || FE.
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Example 2 A.yes B.no C.cannot be determined
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Concept
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Example 3 Use the Triangle Midsegment Theorem A. In the figure, DE and EF are midsegments of ΔABC. Find AB.
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Example 3 Use the Triangle Midsegment Theorem Answer: AB = 10 ED = ABTriangle Midsegment Theorem __ 1 2 5= ABSubstitution __ 1 2 10= ABMultiply each side by 2.
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Example 3 Use the Triangle Midsegment Theorem B. In the figure, DE and EF are midsegments of ΔABC. Find FE.
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Example 3 Use the Triangle Midsegment Theorem Answer: FE = 9 FE = (18)Substitution __ 1 2 1 2 FE = BCTriangle Midsegment Theorem FE = 9Simplify.
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Example 3 Use the Triangle Midsegment Theorem C. In the figure, DE and EF are midsegments of ΔABC. Find m AFE.
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Example 3 Use the Triangle Midsegment Theorem Answer: m AFE = 87 AFE FEDAlternate Interior Angles Theorem m AFE =m FEDDefinition of congruence m AFE =87Substitution By the Triangle Midsegment Theorem, AB || ED.
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Example 3 A.8 B.15 C.16 D.30 A. In the figure, DE and DF are midsegments of ΔABC. Find BC.
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Example 3 B. In the figure, DE and DF are midsegments of ΔABC. Find DE. A.7.5 B.8 C.15 D.16
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Example 3 C. In the figure, DE and DF are midsegments of ΔABC. Find m AFD. A.48 B.58 C.110 D.122
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Concept
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Example 4 Use Proportional Segments of Transversals MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.
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Example 4 Use Proportional Segments of Transversals Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem. Answer: x = 32 Triangle Proportionality Theorem Cross Products Property Multiply. Divide each side by 13.
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Example 4 A.4 B.5 C.6 D.7 In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x.
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Concept
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Example 5 Use Congruent Segments of Transversals ALGEBRA Find x and y. To find x: 3x – 7= x + 5Given 2x – 7= 5Subtract x from each side. 2x= 12Add 7 to each side. x= 6Divide each side by 2.
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Example 5 Use Congruent Segments of Transversals To find y: The segments with lengths 9y – 2 and 6y + 4 are congruent since parallel lines that cut off congruent segments on one transversal cut off congruent segments on every transversal.
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Example 5 Use Congruent Segments of Transversals Answer: x = 6; y = 2 9y – 2 =6y + 4Definition of congruence 3y – 2 =4Subtract 6y from each side. 3y =6Add 2 to each side. y =2Divide each side by 3.
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Example 5 Find a and b. A. ; B.1; 2 C.11; D.7; 3 __ 2 3 3 2
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End of the Lesson
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