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Which of the following statements are true? Select all that apply. 1/2 3/4 9, 7, 8 O A. 23 22 because they are alternate interior angles. O B. mz1+m23 = 180° because they form a straight angle. O C. 23 6 because they are alternate interior angles. O D. 21 and 26 are supplementary because 23 26 and m21 + m23 = 180°. %3D

Which of the following statements are true? Select all that apply. 1/2 3/4 9, 7, 8 O A. 23 22 because they are alternate interior angles. O B. mz1+m23 = 180° because they form a straight angle. O C. 23 6 because they are alternate interior angles. O D. 21 and 26 are supplementary because 23 26 and m21 + m23 = 180°. %3D

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Geometry Standards Review #### Question 6 of 20 **Which of the following statements are true? Select all that apply.** Below is a diagram showing two parallel lines intersected by a transversal. The angles formed are labeled with the numbers 1 through 8. ``` / / 5 /4 | 2 /1 | 3 --/--/--/--/--/-- / / / / / 6/ 7 8/ / ``` **Options:** A. **∠3 ≅ ∠2** because they are alternate interior angles. B. **m∠1 + m∠3 = 180°** because they form a straight angle. C. **∠3 ≅ ∠6** because they are alternate interior angles. D. **∠1 and ∠6 are supplementary** because **∠3 ≅ ∠6** and **m∠1 + m∠3 = 180°**. --- **Explanations:** - **Option A:** **False.** ∠3 and ∠2 are not alternate interior angles. Instead, ∠3 and ∠2 are corresponding angles when the transversal crosses the parallel lines. - **Option B:** **True.** ∠1 and ∠3 together form a linear pair which means their measures add up to 180°. This forms a straight line. - **Option C:** **True.** ∠3 and ∠6 are alternate interior angles when the transversal crosses the parallel lines, thus they are equal. - **Option D:** **False.** While ∠3 ≅ ∠6 is true, ∠1 and ∠6 are not supplementary simply because of this reason. Also, the relation m∠1 + m∠3 = 180° doesn't necessarily make ∠1 and ∠6 supplementary. They are not vertically opposite angles nor do they form a straight line together. --- **Note:** The correctness of each statement relies on understanding the relationships and properties of angles formed by a transversal intersecting parallel lines, such as corresponding angles, alternate interior angles, and supplementary angles.
Transcribed Image Text:### Geometry Standards Review #### Question 6 of 20 **Which of the following statements are true? Select all that apply.** Below is a diagram showing two parallel lines intersected by a transversal. The angles formed are labeled with the numbers 1 through 8. ``` / / 5 /4 | 2 /1 | 3 --/--/--/--/--/-- / / / / / 6/ 7 8/ / ``` **Options:** A. **∠3 ≅ ∠2** because they are alternate interior angles. B. **m∠1 + m∠3 = 180°** because they form a straight angle. C. **∠3 ≅ ∠6** because they are alternate interior angles. D. **∠1 and ∠6 are supplementary** because **∠3 ≅ ∠6** and **m∠1 + m∠3 = 180°**. --- **Explanations:** - **Option A:** **False.** ∠3 and ∠2 are not alternate interior angles. Instead, ∠3 and ∠2 are corresponding angles when the transversal crosses the parallel lines. - **Option B:** **True.** ∠1 and ∠3 together form a linear pair which means their measures add up to 180°. This forms a straight line. - **Option C:** **True.** ∠3 and ∠6 are alternate interior angles when the transversal crosses the parallel lines, thus they are equal. - **Option D:** **False.** While ∠3 ≅ ∠6 is true, ∠1 and ∠6 are not supplementary simply because of this reason. Also, the relation m∠1 + m∠3 = 180° doesn't necessarily make ∠1 and ∠6 supplementary. They are not vertically opposite angles nor do they form a straight line together. --- **Note:** The correctness of each statement relies on understanding the relationships and properties of angles formed by a transversal intersecting parallel lines, such as corresponding angles, alternate interior angles, and supplementary angles.
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