{"id":71250,"date":"2022-06-17T19:32:49","date_gmt":"2022-06-17T14:02:49","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=71250"},"modified":"2022-05-10T12:58:59","modified_gmt":"2022-05-10T07:28:59","slug":"eureka-math-grade-7-module-6-lesson-14","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-7-module-6-lesson-14\/","title":{"rendered":"Eureka Math Grade 7 Module 6 Lesson 14 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 7th Grade Module 6 Lesson 14 Answer Key<\/h2>\n

Eureka Math Grade 7 Module 6 Lesson 14 Example Answer Key<\/h3>\n

Example 1.
\nWhat is the relationship between the two triangles below?
\n\"Engage
\nAnswer:
\nWhat is the relationship between the two triangles below?
\nThe triangles share a common side.
\nImagine that \u25b3WXY and \u25b3WZY were pulled apart and separated. Sketch the triangles separately. Based on how they were joined, what kind of tick mark should be added to each triangle?
\n\\(\\overline{W Y}\\) is a common side. Since it belongs to each triangle, we should put a triple tick mark on \\(\\overline{W Y}\\) to indicate that it is a part of equal measure in both triangles.
\n\"Engage
\nAre the triangles identical? How do you know?
\nThe triangles are identical by the three sides condition. The correspondence that matches the three equal pairs of sides is \u25b3WXY\u2194\u25b3YZW.<\/p>\n

Example 2.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThe triangles are identical by the two sides and the included angle condition. The correspondence \u25b3AOC \u2194 \u25b3BOD matches two equal pairs of sides and a pair of equal angles, \u2220AOC = \u2220BOD, which we know to be equal in measurement because they are vertical angles.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 14 Exercise Answer Key<\/h3>\n

Exercise 1.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThe triangles are not necessarily identical. The correspondence \u25b3QRT \u2194 \u25b3SRT matches a pair of equal angles and a pair of equal sides. The correspondence also matches a common side, \\(\\overline{R T}\\), to both triangles. Two sides and a non-included acute angle do not necessarily determine a unique triangle.<\/p>\n

Exercise 2.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThese triangles are identical by the two angles and side opposite a given angle condition. The correspondence \u25b3EFH \u2194 \u25b3GFH matches two pairs of equal angles and a pair of equal sides. \u2220HFE must be a right angle since \u2220HFG is a right angle, and they are both on a line. Also, \\(\\overline{H F}\\) is a common side to both triangles. Since both triangles have parts under the condition of the same measurement, the triangles must be identical.<\/p>\n

Exercise 3.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThese triangles are identical by the two angles and side opposite a given angle condition. The correspondence \u25b3AOB \u2194 \u25b3COD matches the two pairs of equal angles and one pair of equal sides. There is a marked pair of equal sides and one pair of marked, equal angles. The second pair of equal angles, \u2220AOB = \u2220COD, are vertical angles.<\/p>\n

Exercise 4.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThe triangles are not necessarily identical. The correspondence \u25b3AEB \u2194 \u25b3CED matches three pairs of equal angles, including the unmarked angles, \u2220AEB and \u2220CED, which are equal in measurement because they are vertical angles. The triangles could have different side lengths; therefore, they are not necessarily identical.<\/p>\n

Exercise 5.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThe triangles are identical by the two sides and non-included 90\u00b0 (or greater) angle condition. The correspondence \u25b3MPO \u2194 \u25b3NPO matches two pairs of equal sides and one pair of equal angles. One of the two pairs of equal sides is side \\(\\overline{O P}\\), which is common to both triangles.<\/p>\n

Exercise 6.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThese triangles are not necessarily identical. The triangles have a pair of marked equal sides and equal angles; side \\(\\overline{C E}\\) is also common to both triangles. The triangles satisfy the two sides and non-included acute angle condition, which does not determine a unique triangle.<\/p>\n

Exercise 7.
\nAre the triangles identical? Justify your reasoning.
\n\"Engage
\nAnswer:
\nThese triangles are identical by the two angles and a side opposite a given angle condition. The triangle correspondence \u25b3RWS \u2194 \u25b3RWT matches two pairs of equal angles and one pair of equal sides. The equal pair of sides, \\(\\overline{R W}\\), is common to both triangles.<\/p>\n

Exercise 8.
\nCreate your own labeled diagram and set of criteria for a pair of triangles. Ask a neighbor to determine whether the triangles are identical based on the provided information.
\nAnswer:
\nAnswers will vary.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 14 Problem Set Answer Key<\/h3>\n

In the following problems, determine whether the triangles are identical, not identical, or not necessarily identical; justify your reasoning. If the relationship between the two triangles yields information that establishes a condition, describe the information. If the triangles are identical, write a triangle correspondence that matches the sides and angles.
\nQuestion 1.
\n\"Eureka
\nAnswer:
\nThese triangles are identical by the two sides and the included angle condition. The triangle correspondence \u25b3ABC \u2194 \u25b3ADC matches two pairs of equal sides and one pair of equal angles. One of the equal pairs of sides is shared side \\(\\overline{A C}\\).<\/p>\n

Question 2.
\n\"Eureka
\nAnswer:
\nThese triangles are not necessarily identical. The triangles have a pair of marked equal sides, and a pair of marked, acute, equal angles; side \\(\\overline{A C}\\) is also common to both triangles. The triangles satisfy the two sides and non-included acute angle condition, which does not determine a unique triangle.<\/p>\n

Question 3.
\n\"Eureka
\nAnswer:
\nThese triangles are identical by the two angles and included side condition. The triangle correspondence \u25b3QPR \u2194 \u25b3TSR matches the two pairs of equal angles and one pair of equal sides. One pair of equal angles is the vertical angle pair \u2220PRQ = \u2220SRT.<\/p>\n

Question 4.
\n\"Eureka
\nAnswer:
\nThese triangles are not necessarily identical. A correspondence that matches up the equal pair of sides and the equal pair of vertical angles does not match the marked equal pair of angles.<\/p>\n

Question 5.
\n\"Eureka
\nAnswer:
\nThe triangles are identical by the two sides and non-included 90\u00b0 (or greater) angle condition. The correspondence \u25b3IFG \u2194 \u25b3GHI matches two pairs of equal sides and one pair of equal angles. One of the two pairs of equal sides is side \\(\\overline{I G}\\), which is common to both triangles.<\/p>\n

Question 6.
\n\"Eureka
\nAnswer:
\nThe triangles are not identical since a correspondence that matches the two marked equal pairs of sides also matches sides \\(\\overline{V X}\\) and \\(\\overline{X Y}\\), which are not equal in length.<\/p>\n

Question 7.
\n\"Eureka
\nAnswer:
\nThese triangles are identical by the two angles and side opposite a given angle condition. The correspondence \u25b3ABD \u2194 \u25b3CBD matches the two pairs of equal angles and one pair of equal sides. The pair of equal sides is the common side, \\(\\overline{B D}\\). We know \u2220ADB must be a right angle since \u2220CDB is a right angle; they are both on a line, and of course angles \u2220A and \u2220C are equal in measurement.<\/p>\n

Question 8.
\nAre there any identical triangles in this diagram?
\n\"Eureka
\nAnswer:
\n\u25b3TUX and \u25b3VWX are not necessarily identical; we only know about a single pair of equal angles in the triangles, which are vertical angles. \u25b3TUV and \u25b3VWT are also not necessarily identical. We only know about a single pair of equal angles and a side common to both triangles, which is not enough information to determine the triangles as identical or non-identical.<\/p>\n

Question 9.
\n\"Eureka
\nAnswer:
\nThe triangles are not necessarily identical since there is no correspondence that matches the two marked equal pairs of sides as well as the two pairs of equal angles. One of the pairs of equal angles is the pair of vertical angles.<\/p>\n

Question 10.
\n\"Eureka
\nAnswer:
\n\u25b3ABE and \u25b3CBD are not necessarily identical. The triangles satisfy the two sides and non-included acute angle condition, which does not determine a unique triangle.<\/p>\n

Eureka Math Grade 7 Module 6 Lesson 14 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nAre \u25b3DEF and \u25b3DGF identical, not identical, or not necessarily identical? Justify your reasoning. If the relationship between the two triangles yields information that establishes a condition, describe the information. If the triangles are identical, write a triangle correspondence that matches the sides and angles.
\n\"Eureka
\nAnswer:
\nThese triangles are identical by the two angles and side opposite a given angle condition. The triangle correspondence \u25b3DEF \u2194 \u25b3DGF matches the two pairs of equal angles and one pair of equal sides condition. The pair of equal sides, \\(\\overline{D F}\\), is common to both triangles.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 7th Grade Module 6 Lesson 14 Answer Key Eureka Math Grade 7 Module 6 Lesson 14 Example Answer Key Example 1. What is the relationship between the two triangles below? Answer: What is the relationship between the two triangles below? The triangles share a common side. Imagine that \u25b3WXY and \u25b3WZY … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/71250"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=71250"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/71250\/revisions"}],"predecessor-version":[{"id":137953,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/71250\/revisions\/137953"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=71250"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=71250"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=71250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}