Geom_10.29 Review

In Euclidean geometry, the sum of the interior angles of a triangle is 180°. Which of the following describes the sum (x) of the interior angles in spherical geometry?

• 180 < x < 540

• 180 ≤ x ≤ 540

• 540 < x < 180

• 180 > x > 540

Which of the following cannot be the sum of the measures of the angles in a triangle in spherical geometry? Select all that apply.

(a)   (b)  

• 245°

• 180°
• 270°

• 120°
• 185°

Karla is working on her assignment. She needs to explain why the two circles on the sphere are NOT examples of parallel lines. Which of the following is an accurate explanation?

• The two circles are not an example of parallel lines because they are not congruent.

• The two circles are not an example of parallel lines because the smaller circle must be located above the great circle.

• The two circles are not an example of parallel lines because the smaller circle is not a great circle and therefore it is not a line in spherical geometry.

• The two circles are not an example of parallel lines because they both are latitudes of the sphere instead of one latitude and one longitude.

Answer explanation

In Euclidean Geometry=for any line and point not on the line, there exist one parallel line that passes through the point.

In Spherical Geometry=for any line and point not on the line, no parallel line exists.

Relationships of lines and angles are different in Euclidean and Spherical geometries. A relationship that is considered true in Euclidean geometry may not be true in Spherical geometry. Which of the following statements are true in Spherical geometry? Select all that apply.

• A triangle can have only one right angle.

• Through any two points there is exactly one line.

• Two perpendicular lines form eight 90° angles.

• Equilateral triangles have three angles measuring 60° each.

• Vertical angles are congruent.

Tags

CCSS.8.G.A.2

Two airplanes follow flight paths around the globe along different great circles. How many times will the flight paths intersect?

(a)  

• 1 time

• 2 times
• 3 times

• infinitely many

ΔABC is transformed as shown on the graph. Which transformation notation accurately describes the sequence of transformations that were applied to ΔABC to obtain ΔA′B′C′?

• (x, y) → (x + 11, y + 5)

• (x, y) → (x − 11, y − 5)

• (x, y) → (x + 11, y − 5)

• (x, y) → (x − 11, y + 5)

Tags

CCSS.HSG.CO.A.2

Polygon ABCD is to be translated using the function rule T_{⟨6, -4⟩}(ABCD) = A′B′C′D′. Determine the coordinates of the image.

• A′(6, -4), B′(3, 4), C′(-2, 4), D′(-2, -3)

• A′(-3, -4), B′(-2, 3), C′(4, 2), D′(3, 2)

• A′(-3, 3), B′(4, 3), C′(4, -2), D′(-3, -2)

• A′(-6, -2), B′(-2, -3), C′(2, 7), D′(3, -2)

Tags

CCSS.HSG.CO.A.2

Which algebraic representation indicates reflecting a shape across the x-axis and then translating the shape right 4 units and down 3 units on the coordinate plane?

(a)  

• (x − 4, −y − 3)

• (x + 4, −y − 3)
• (−x + 4, y − 3)

• (−x − 4, y − 3)

Tags

CCSS.HSG.CO.A.2

The coordinates of ΔLMN are L(3,-5), M(8,4), and N(5,2). A reflection maps L to L'(-3, -5). Describe the transformation using a notation, then determine the coordinates of M' and N'.

The transformation is: (a)   and the coordinates of M' and N' are​ (b)  

• Ry-axis(LMN)=L'M'N'
• Rx-axis(LMN)=L'M'N'
• Ry-axis(L'M'N')=LMN
• Rx-axis(L'M'N')=LMN
• M'(-8, 4), N'(-5, 2)
• M'(4, -8), N'(2, -5)
• M'(-3, -5), N'(-5, -3)
• M'(4, 8), N'(2,5)
• M'(-4, -8), N'(-2, -5)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which of the images on the graph accurately models the result of a composition of transformation described by R_y−axis(x, y) and T_{⟨−3, −8⟩}(x′, y′).

(a)  

• Image A

• Image B
• Image C

• Image D

Tags

CCSS.8.G.A.3