Geom Benchmark #2 Review (no calc)

Geometry Benchmark #2 Review

NO Calculator Part

Multiple Choice

A student correctly reflects rectangle 𝑯𝑱𝑲𝑳 across the line 𝒙=𝟏 and forms rectangle 𝑯′𝑱′𝑲′𝑳′. Which graph represents this scenario?

Multiple Choice

Triangle 𝑯𝑱𝑲 is rotated clockwise to form triangle 𝑿𝒀𝒁.

What additional information is needed to prove triangle 𝑯𝑱𝑲 is congruent to triangle 𝑿𝒀𝒁 by the Side-Angle-Side congruence theorem?

• 𝑋𝑌=4 units and m∠𝑌=135°

• 𝑋𝑌=4 units and m∠𝑍=135°

• 𝑋𝑍=4 units and m∠𝑌=135°

• 𝑋𝑍=4 units and m∠𝑍=135°

Multiple Choice

Consider $$\Delta KGH$$ , where $$\frac{KU}{UG}=\frac{KV}{VH}$$ .

If a student correctly proves 𝑼𝑽||𝑮𝑯, which statement could the student write as a step in the proof?

• ∠𝐾𝑈𝑉≅∠𝐾𝑉𝑈

• ∠𝐾𝑈𝑉≅∠𝑉𝑈𝐺

• ∠𝑉𝐾𝑈≅∠𝐾𝐺𝐻

• ∠𝑉𝐾𝑈≅∠VKU

Multiple Choice

Consider the measurements of triangle 𝑻𝑽𝑼.

If triangle 𝑻𝑽𝑼 undergoes a series of rigid transformations and maps onto triangle 𝑿𝒀𝒁, which statement must be true?

• 𝑋𝑌=6 mm, 𝑋𝑍=25.4 mm, 𝑌𝑍=26.6 mm, m∠𝑋=13°, m∠𝑌=72°, and m∠𝑍=95°.

• 𝑋𝑌=6 mm, 𝑋𝑍=25.4 mm, 𝑌𝑍=26.6 mm, m∠𝑋=72°, m∠𝑌=13°, and m∠𝑍=95°.

• 𝑋𝑌=26.6 mm, 𝑋𝑍=25.4 mm, 𝑌𝑍=6 mm, m∠𝑋=13°, m∠𝑌=72°, and m∠𝑍=95°.

• 𝑋𝑌=26.6 mm, 𝑋𝑍=25.4 mm, 𝑌𝑍=6 mm, m∠𝑋=72°, m∠𝑌=13°, and m∠𝑍=95°.

Multiple Choice

Consider the circle with center 𝑲.

If circle 𝑲 is rotated 𝟐𝟕𝟎° counterclockwise about the origin and then translated down 𝟑 units to form circle 𝑲′, which statement is true?

• Circle 𝐾 is congruent to circle 𝐾′ because rotations and translations are both nonrigid transformations.

• Circle 𝐾 is congruent to circle 𝐾′ because rotations and translations are both rigid transformations.

• Circle 𝐾 is not congruent to circle 𝐾′ because rotations and translations are both nonrigid transformations.

• Circle 𝐾 is not congruent to circle 𝐾′ because rotations and translations are both rigid transformations.

Multiple Choice

If 𝐜𝐨𝐬(𝟒𝒙)=𝐬𝐢𝐧(𝟑𝟎°+𝟐𝒙), and 𝟎°<𝟒𝒙<𝟗𝟎°, what is the value of 𝒙?

• 10

• 15

• 30

• 60

Multiple Choice

Trapezoid 𝑹𝑺𝑻𝑼 is rotated 𝟗𝟎° clockwise about vertex 𝑺 to form trapezoid 𝑹′𝑺′𝑻′𝑼′.

What are the coordinates of trapezoid 𝑹′𝑺′𝑻′𝑼′?

• 𝑅′(−2,−3), 𝑆′(−2,1), 𝑇′(2,1), 𝑈′(2,−5)

• 𝑅′(−2,5), 𝑆′(−2,1), 𝑇′(−6,1), 𝑈′(−6,8)

• 𝑅′(−1,−6), 𝑆′(−1,−2), 𝑇′(3,−2), 𝑈′(3,−9)

• 𝑅′(1,6), 𝑆′(1,2), 𝑇′(−3,2), 𝑈′(−3,9)

Multiple Choice

Consider the coordinates of three vertices of a square.

(−𝟏,𝟔), (𝟐,𝟐), and (−𝟐,−𝟏)

Which could be the coordinates of the fourth vertex?

• (-5,2)

• (-5,3)

• (-4,2)

• (-4,3)

Multiple Choice

Consider the two triangles.

For which sequence of transformations would triangle 𝑿𝒀𝒁 have image 𝑿′𝒀′𝒁′?

• a 270° clockwise rotation about the origin followed by a translation down 2 units

• a 270° clockwise rotation about the origin followed by a translation right 1 unit

• a 270° counterclockwise rotation about the origin followed by a translation down 2 units

• a 270° counterclockwise rotation about the origin followed by a translation right 1 unit

Multiple Choice

A parallelogram is translated vertically and then horizontally on the coordinate plane. Which statement is true?

• Both pairs of opposite sides of the image will be parallel because translations preserve all parallel lines.

• Only one pair of opposite sides of the image will be parallel because translations preserve some parallel lines.

• The image will have no pairs of parallel sides because translations do not preserve parallel lines.

• The image will have no pairs of parallel sides because translations preserve all parallel lines.

Multiple Choice

Consider $$\Delta SWL$$ , where 𝑷𝑹 is parallel to 𝑺𝑳. If a student correctly proves $$\frac{WP}{WS}=\frac{WR}{WL}$$ , which statement could the student write as a step in the proof?

• Triangle SWL~Triangle PWR

• Triangles SWL ~ TRaingle RWP

• TRiangle WSL ~ Triangle PWR

• TRiangle WSL ~ Trianlge RWP