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Addition Properties 1) Define a two-column proof. An organized method that shows statements and reasons to support geometric statements about a theorem. 3897 character(s) left Your answer is too long. Correct! Attachments There are no attachments 2) Review Angle Addition (Postulate 1-B) and then fill in the blanks in the following statement: If ray QR is located in the interior of angle PQS, then the measurement of angle ____ + the measurement of angle ____ = the measurement of angle PQS. 223 character(s) left Your answer is too long. Correct! 3) Refer to Theorem 5-B and the figure shown below to answer the following questions: If the measure of angle QPR = 23 degrees and the measure of angle NPQ = 48 degrees, (a) what is the measure of angle NPR and (b) what is the measure of angle QPS? 221 character(s) left Your answer is too long. Correct! Now you will take an in-depth look at the proof for Theorem 5-B. Study the proof for Theorem 5-A found in the unit link to “Addition Properties”. The proof for Theorem 5-A will serve as a good model for completing the proof of Theorem 5-B below. First, copy or print the partially completed proof, complete the proof, and then answer the next five questions. Select the reasons from the following list: “Substitution Property of Equality”, “Definition of Congruence”, Angle Addition (Postulate 1-B)”, “Addition Property of Equality”. Some reasons may be used more than once. 4) What is the reason for statement #2? 225 character(s) left Your answer is too long. Correct! 5) What is the reason for statement #3? 220 character(s) left Your answer is too long. Correct! 6) What is the reason for statement #4? 233 character(s) left Your answer is too long. Incorrect 7) What is the reason for statement #5? 216 character(s) left Your answer is too long. Correct! 8) What is the reason for statement #6? 225 character(s) left Your answer is too long. Correct! 9) Now that you have completed the proof of Theorem 5-B, briefly explain the main idea of this theorem in your own words. The angle sums are congruent if added together. 3952 character(s) left Your answer is too long. Correct! Attachments There are no attachments Copy or print the next partially completed proof, complete the proof, and then answer the next six questions. 10) What is the statement in step #1? AB ~= FG, BC~= EF 3983 character(s) left Your answer is too long. Correct! Missing the first half of it. 11) What is the reason for statement #2? 225 character(s) left Your answer is too long. Correct! 12) What is the reason for statement #3? 220 character(s) left Your answer is too long. Correct! 13) What is the reason for statement #4? 223 character(s) left Your answer is too long. Incorrect 14) What is the statement for step #5? 236 character(s) left Your answer is too long. Incorrect 15) What is the final statement (conclusion) for step #6? 242 character(s) left Your answer is too long. Incorrect 16) Now that you have completed the proof of Theorem 5-C, briefly explain the main idea of this theorem in your own words. this is used in proofs with congruent triangles its the segment addition postulate and the properties of equality. 3885 character(s) left Your answer is too long. Incorrect Attachments There are no attachments Subtraction Properties 17) Read and study Theorem 5-G, and then briefly explain the main idea of this theorem in your own words. if two segments are subtracted their differences are congruent 3937 character(s) left Your answer is too long. Correct! Attachments There are no attachments Refer to the figure below to answer the next two questions. 18) What information is given? (Hint: Make statements regarding the segments that are marked with “hash marks”.) segment BDA is congruent to segment BEC, BA is congruent to BC and AC is also congruent to BA and BC 3900 character(s) left Your answer is too long. Incorrect Missing the second half 19) If segment AD is subtracted from segment AB and segment CE is subtracted from segment CB, what is true about segment BD and BE. a.) BD > BE b.) BD < BD c.) BD = BE d.) No relationship can be determined. Correct! 20) Read and study Theorem 5-H, and then briefly explain the main idea of this theorem in your own words. Two congruent segments differences are congruent 3951 character(s) left Your answer is too long. Correct! Attachments There are no attachments Refer to the figure below to answer the next three questions. 21) State the angles that are congruent based on “hash marks” shown on the figure. Angle RTS are congruent to Angle QRT, and angles QTS are congruent to QRS. As well as angles QTR being congruent to SRT 3881 character(s) left Your answer is too long. Correct! 22) If angle QRS is subtracted from angle QRT and angle STQ is subtracted from angle STR, what are the names of the two congruent angles that are the result of finding the differences? a.) There are none. b.) angles QRS and QRT c.) angles RST and TQR d.) angles SRT and QTR Correct! 23) If the measure of angle QRT = 115 degrees, and the measure of angle QRS = 80 degrees, what is the measure of angle QTR? 248 character(s) left Your answer is too long. Correct! 24) Based on the given information and any “subtraction property” theorems, how can you deduce that angle 7 must measure 35 degrees? since angles QRP and angles TRS are congruent that means the angles must equal the same. Since angle 8 equals 90 degrees then angles 7 and 9 have to equal 45 degrees. 3834 character(s) left Your answer is too long. Correct! Attachments There are no attachments Multiplication and Division Properties 25) Which of the terms mean to divide a geometric shape into three equal parts? a.) monomial b.) bisect c.) trisect d.) polynomial Correct! 26) Which of the terms mean to divide a geometric shape into two equal parts? a.) monomial b.) bisect c.) trisect d.) polynomial Correct! Draw a diagram to represent the following geometric figure, and then answer the next six questions: On Segment KN, points L and M are collinear with K and N and fall between points K and N. Point L is closer to point K than point M. Points L and M trisect segment KN. 27) State all segments that are 1/3 the length of segment KN. 242 character(s) left Your answer is too long. Correct! 28) State all segments that are 2/3 the length of segment KN. 238 character(s) left Your answer is too long. Incorrect 29) If Segment KL measures 17 cm, what is the measure of segment KN? 248 character(s) left Your answer is too long. Correct! 30) If Segment LN measures 15 cm, what is the measure of segment MN? 245 character(s) left Your answer is too long. Incorrect 31) If segment KM measures 16.9 cm, what is the measure of segment LN? 242 character(s) left Your answer is too long. Correct! 32) If segment KN measures 10 cm, what is the measure of segment LN? 242 character(s) left Your answer is too long. Correct! 33) Select the term that fills in the blank in the following statement: If point P is placed as a midpoint between points L and M, then point P _____________ segment LM. a.) bisects b.) trisects Correct! Draw a diagram to represent the following geometric figure, and then answer the next two questions: Angle TOV is an obtuse angle that measures 145 degrees. Ray OM bisects angle TOV. 34) Name the two congruent angles. 239 character(s) left Your answer is too long. Correct! 35) What is the measure of angle TOM? 246 character(s) left Your answer is too long. Correct! Proofs A good definition is reversible. For the next two problems, good definitions are given. Read the definition, and then complete the reverse of the definition. 36) An acute angle is an angle that measures less than 90 degrees. An angle that measures less than 90 degrees is ___________________________. 235 character(s) left Your answer is too long. Correct! 37) Non-collinear points are three or more points that do not lie on the same line. Three or more points that do not lie on the same line are ___________________________. 229 character(s) left Your answer is too long. Correct! 38) Examine this poorly constructed definition: “Complementary angles total 90 degrees”. Rephrase the definition so that it is reversible. (a) Write the new definition and (b) write its reverse. 2 angles that equal 90 degrees are complementary complementary angles are 2 angles that equal 90 degrees 3894 character(s) left Your answer is too long. Correct! 39) Write a proof for the given information and the conclusion. You may write the proof in paragraph form or you can write a formal proof using statements and reasons. If you decide to write a formal proof, you may complete the proof in a word-processing document and attach it below. if two angles of a triangle are congruent to angles of another triangles, then the triangles are similar. 19894 character(s) left Your answer is too long. Incorrect Attachments There are no attachments 40) Write a proof for the given information and the conclusion. You may write the proof in paragraph form or you can write a formal proof using statements and reasons. If you decide to write a formal proof, you may complete the proof in a word-processing document and attach it below. ABD are congruent to CBE because they equal the same thing 19941 character(s) left Your answer is too long. Incorrect Attachments There are no attachments 41) Write a proof for the given information and the conclusion. You may write the proof in paragraph form or you can write a formal proof using statements and reasons. If you decide to write a formal proof, you may complete the proof in a word-processing document and attach it below. Angle HKN is a reflection of angle HJN 19962 character(s) left Your answer is too long. Incorrect Attachments There are no attachments 42) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. DATE START TIME END TIME DESCRIPTION 11/21/2023 03:40 PM 04:24 PM Read and took notes. 0 Hour(s) & 44 Minute(s) Correct! Attachments There are no attachments