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Unit 3 Assessment

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Geometry
Unit 3 Assessment
1.
Name___________________
Date________________
Period_________
Lines 𝑅𝑃, π‘‰π‘Š, and 𝑀𝑆 are shown. βƒ‘π‘‰π‘Š intersects
⃑𝑅𝑃 at point 𝐻. βƒ‘π‘‰π‘Š intersects ⃑𝑀𝑆 at point 𝐺.
First, determine if each condition is sufficient on
⃑ . Then, write a
⃑ βˆ₯ 𝑀𝑆
its own to show that 𝑅𝑃
justification.
Condition
Sufficient to
show that
⃑𝑹𝑷 βˆ₯ ⃑𝑴𝑺?
a.
βˆ π‘ƒπ»πΊ β‰… βˆ π‘€πΊπ»
 Yes
 No
b.
βˆ π‘…π»πΊ and βˆ π‘€πΊπ»
are supplementary.
 Yes
 No
c.
βˆ π‘†πΊπ‘Š β‰… βˆ π‘ƒπ»π‘‰
 Yes
 No
d.
π‘šβˆ π‘ŠπΊπ‘€ β‰… π‘šβˆ πΊπ»π‘…
 Yes
 No
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Justification
2.
Four angles are shown where βˆ π‘π»π· is complementary to βˆ π‘‹π‘‡π‘€, βˆ πΎπ‘…πΆ is
supplementary to βˆ πΆπ‘Œπ‘Š, and
βˆ πΎπ‘…πΆ is complementary to
βˆ π‘π»π·. π‘šβˆ πΆπ‘Œπ‘Š = 11π‘₯ βˆ’ 27,
π‘šβˆ π‘‹π‘‡π‘€ = 3π‘₯ + 11, and
π‘šβˆ π‘π»π· = 2π‘₯ + 9.
Select all of the statements
that are true based on the
given information.
 π‘šβˆ π‘‹π‘‡π‘€ = π‘šβˆ πΎπ‘…πΆ
 3π‘₯ + 11 + 2π‘₯ + 9 = 90°
 11π‘₯ βˆ’ 27 + 2π‘₯ + 9 = 180°
 π‘šβˆ π‘‹π‘‡π‘€ + π‘šβˆ πΆπ‘Œπ‘Š = 180°
 11π‘₯ βˆ’ 27 + 3π‘₯ + 11 + 2π‘₯ + 9 = 180°
3.
⃑ βˆ₯ π΅π‘Œ
⃑ , βƒ‘πΉπ‘Š βˆ₯ ⃑𝑋𝑇, π‘šβˆ π‘‹πΏπ‘ = 100°, π‘šβˆ π‘π»πΎ = 34°,
A diagram is shown where 𝐿𝐾
and π‘šβˆ π‘Œπ΅π» = 107°.
Complete the table.
a.
π‘šβˆ πΎπ‘Œπ΅ =_______
b.
π‘šβˆ π‘‹πΏπΉ =_______
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4.
Parallel lines ⃑𝐿𝑁, ⃑𝐡𝐻, and ⃑𝑅𝐾, with a transversal βƒ‘π‘ƒπ‘Š , are shown π‘šβˆ π΅π‘€π‘‰ =
108° and π‘šβˆ πΎπ‘‰π‘† = 72°.
Complete the table.
5.
a.
π‘šβˆ π‘Šπ‘ƒπ‘ =_______
b.
π‘šβˆ πΏπ‘ƒπ‘Š =_______
Parallel lines βƒ‘π΅π‘Š and ⃑𝐷𝑀 are
shown where π‘šβˆ π‘‹π·π‘€ = 138°
and π‘šβˆ π»π΅π‘Š = 29°.
Complete the table.
a.
π‘šβˆ πΆπ‘Šπ΅ =_______
b.
π‘šβˆ π»π‘€π‘Œ =_______
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6.
An engineer is designing a parking lot for a local grocery store. The
parking spaces are marked with lines where ⃑𝑋𝐷 βˆ₯ ⃑𝑇𝑍 βˆ₯ βƒ‘π‘ŒπΉ βˆ₯ ⃑𝐿𝑃 where βƒ‘π‘ŠπΆ
is a transversal, as shown, where π‘šβˆ πΆπ‘πΏ = (6π‘₯ βˆ’ 17.6)°, π‘šβˆ πΉπ΅π» = (12𝑦 βˆ’
22)°, and π‘šβˆ π‘‡π»π‘… = (3π‘₯ + 29.2)°.
a. Determine the value of π‘₯.
𝒙=
b. Determine the value of 𝑦.
π’š=
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7.
A diagram is shown where ⃑𝑃𝐿
intersects lines 𝐡𝐻, 𝐾𝐺, and 𝑅𝐹.
⃑ βˆ₯ 𝑅𝐹
⃑ , βˆ π»π‘‹π‘Š β‰… βˆ π‘Œπ‘ŠπΊ
Given: 𝐡𝐻
⃑
⃑ βˆ₯ 𝐾𝐺
Prove: 𝑅𝐹
Complete the proof.
Statement
Reason
⃑ βˆ₯ 𝑅𝐹
⃑
1. 𝐡𝐻
1. Given
2.
2.
3. βˆ π»π‘‹π‘Š β‰… βˆ π‘Œπ‘ŠπΊ
3. Given
4.
4.
5. ⃑𝑅𝐹 βˆ₯ ⃑𝐾𝐺
5.
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