Geometry Unit 3 Assessment 1. Name___________________ Date________________ Period_________ Lines π π, ππ, and ππ are shown. β‘ππ intersects β‘π π at point π». β‘ππ intersects β‘ππ at point πΊ. First, determine if each condition is sufficient on β‘ . Then, write a β‘ β₯ ππ its own to show that π π justification. Condition Sufficient to show that β‘πΉπ· β₯ β‘π΄πΊ? a. β ππ»πΊ β β ππΊπ» ο― Yes ο― No b. β π π»πΊ and β ππΊπ» are supplementary. ο― Yes ο― No c. β ππΊπ β β ππ»π ο― Yes ο― No d. πβ ππΊπ β πβ πΊπ»π ο― Yes ο― No Math Nation © Justification 2. Four angles are shown where β ππ»π· is complementary to β πππ, β πΎπ πΆ is supplementary to β πΆππ, and β πΎπ πΆ is complementary to β ππ»π·. πβ πΆππ = 11π₯ β 27, πβ πππ = 3π₯ + 11, and πβ ππ»π· = 2π₯ + 9. Select all of the statements that are true based on the given information. ο― πβ πππ = πβ πΎπ πΆ ο― 3π₯ + 11 + 2π₯ + 9 = 90° ο― 11π₯ β 27 + 2π₯ + 9 = 180° ο― πβ πππ + πβ πΆππ = 180° ο― 11π₯ β 27 + 3π₯ + 11 + 2π₯ + 9 = 180° 3. β‘ β₯ π΅π β‘ , β‘πΉπ β₯ β‘ππ, πβ ππΏπ = 100°, πβ ππ»πΎ = 34°, A diagram is shown where πΏπΎ and πβ ππ΅π» = 107°. Complete the table. a. πβ πΎππ΅ =_______ b. πβ ππΏπΉ =_______ Math Nation © 4. Parallel lines β‘πΏπ, β‘π΅π», and β‘π πΎ, with a transversal β‘ππ , are shown πβ π΅ππ = 108° and πβ πΎππ = 72°. Complete the table. 5. a. πβ πππ =_______ b. πβ πΏππ =_______ Parallel lines β‘π΅π and β‘π·π are shown where πβ ππ·π = 138° and πβ π»π΅π = 29°. Complete the table. a. πβ πΆππ΅ =_______ b. πβ π»ππ =_______ Math Nation © 6. An engineer is designing a parking lot for a local grocery store. The parking spaces are marked with lines where β‘ππ· β₯ β‘ππ β₯ β‘ππΉ β₯ β‘πΏπ where β‘ππΆ is a transversal, as shown, where πβ πΆππΏ = (6π₯ β 17.6)°, πβ πΉπ΅π» = (12π¦ β 22)°, and πβ ππ»π = (3π₯ + 29.2)°. a. Determine the value of π₯. π= b. Determine the value of π¦. π= Math Nation © 7. A diagram is shown where β‘ππΏ intersects lines π΅π», πΎπΊ, and π πΉ. β‘ β₯ π πΉ β‘ , β π»ππ β β πππΊ Given: π΅π» β‘ β‘ β₯ πΎπΊ Prove: π πΉ Complete the proof. Statement Reason β‘ β₯ π πΉ β‘ 1. π΅π» 1. Given 2. 2. 3. β π»ππ β β πππΊ 3. Given 4. 4. 5. β‘π πΉ β₯ β‘πΎπΊ 5. Math Nation ©