Geometry
Unit 3 Assessment
1.
Name___________________
Date________________
Period_________
Lines 𝑅𝑃, 𝑉𝑊, and 𝑀𝑆 are shown. ⃡𝑉𝑊 intersects
⃡𝑅𝑃 at point 𝐻. ⃡𝑉𝑊 intersects ⃡𝑀𝑆 at point 𝐺.
First, determine if each condition is sufficient on
⃡ . Then, write a
⃡ ∥ 𝑀𝑆
its own to show that 𝑅𝑃
justification.
Condition
Sufficient to
show that
⃡𝑹𝑷 ∥ ⃡𝑴𝑺?
a.
∠𝑃𝐻𝐺 ≅ ∠𝑀𝐺𝐻
 Yes
 No
b.
∠𝑅𝐻𝐺 and ∠𝑀𝐺𝐻
are supplementary.
 Yes
 No
c.
∠𝑆𝐺𝑊 ≅ ∠𝑃𝐻𝑉
 Yes
 No
d.
𝑚∠𝑊𝐺𝑀 ≅ 𝑚∠𝐺𝐻𝑅
 Yes
 No
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Justification
2.
Four angles are shown where ∠𝑁𝐻𝐷 is complementary to ∠𝑋𝑇𝑀, ∠𝐾𝑅𝐶 is
supplementary to ∠𝐶𝑌𝑊, and
∠𝐾𝑅𝐶 is complementary to
∠𝑁𝐻𝐷. 𝑚∠𝐶𝑌𝑊 = 11𝑥 − 27,
𝑚∠𝑋𝑇𝑀 = 3𝑥 + 11, and
𝑚∠𝑁𝐻𝐷 = 2𝑥 + 9.
Select all of the statements
that are true based on the
given information.
 𝑚∠𝑋𝑇𝑀 = 𝑚∠𝐾𝑅𝐶
 3𝑥 + 11 + 2𝑥 + 9 = 90°
 11𝑥 − 27 + 2𝑥 + 9 = 180°
 𝑚∠𝑋𝑇𝑀 + 𝑚∠𝐶𝑌𝑊 = 180°
 11𝑥 − 27 + 3𝑥 + 11 + 2𝑥 + 9 = 180°
3.
⃡ ∥ 𝐵𝑌
⃡ , ⃡𝐹𝑊 ∥ ⃡𝑋𝑇, 𝑚∠𝑋𝐿𝑁 = 100°, 𝑚∠𝑁𝐻𝐾 = 34°,
A diagram is shown where 𝐿𝐾
and 𝑚∠𝑌𝐵𝐻 = 107°.
Complete the table.
a.
𝑚∠𝐾𝑌𝐵 =_______
b.
𝑚∠𝑋𝐿𝐹 =_______
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4.
Parallel lines ⃡𝐿𝑁, ⃡𝐵𝐻, and ⃡𝑅𝐾, with a transversal ⃡𝑃𝑊 , are shown 𝑚∠𝐵𝑀𝑉 =
108° and 𝑚∠𝐾𝑉𝑆 = 72°.
Complete the table.
5.
a.
𝑚∠𝑊𝑃𝑁 =_______
b.
𝑚∠𝐿𝑃𝑊 =_______
Parallel lines ⃡𝐵𝑊 and ⃡𝐷𝑀 are
shown where 𝑚∠𝑋𝐷𝑀 = 138°
and 𝑚∠𝐻𝐵𝑊 = 29°.
Complete the table.
a.
𝑚∠𝐶𝑊𝐵 =_______
b.
𝑚∠𝐻𝑀𝑌 =_______
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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 ∥ ⃡𝑇𝑍 ∥ ⃡𝑌𝐹 ∥ ⃡𝐿𝑃 where ⃡𝑊𝐶
is a transversal, as shown, where 𝑚∠𝐶𝑁𝐿 = (6𝑥 − 17.6)°, 𝑚∠𝐹𝐵𝐻 = (12𝑦 −
22)°, and 𝑚∠𝑇𝐻𝑅 = (3𝑥 + 29.2)°.
a. Determine the value of 𝑥.
𝒙=
b. Determine the value of 𝑦.
𝒚=
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7.
A diagram is shown where ⃡𝑃𝐿
intersects lines 𝐵𝐻, 𝐾𝐺, and 𝑅𝐹.
⃡ ∥ 𝑅𝐹
⃡ , ∠𝐻𝑋𝑊 ≅ ∠𝑌𝑊𝐺
Given: 𝐵𝐻
⃡
⃡ ∥ 𝐾𝐺
Prove: 𝑅𝐹
Complete the proof.
Statement
Reason
⃡ ∥ 𝑅𝐹
⃡
1. 𝐵𝐻
1. Given
2.
2.
3. ∠𝐻𝑋𝑊 ≅ ∠𝑌𝑊𝐺
3. Given
4.
4.
5. ⃡𝑅𝐹 ∥ ⃡𝐾𝐺
5.
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